Let's Stick Together? The Impact of Collectivism on COVID-19 Spread and the Effectiveness of Non-Pharmaceutical Government Interventions

TABLE OF CONTENTS

1. Extracting Data

1.1. Extracting indicators from the World Bank

1.2. Merging metrics, cases, and Hofstede index

1.2.1. Extracting case data

1.2.2. Hofstede Index

1.2.3. Merging data

1.3. Mobility Data

1.3.1. Extracting mobility data

1.3.2. Plotting mobility data

1.4. Testing data

1.5. Governmental response

1.6. Regime Type

1.7. Distance from WUHAN

2. COVID-19 and Individualism EDA

2.1. Getting COVID-19 data per month

2.2. Getting COVID-19 data by month for a number of countries

3. Cleaning the data

3.1. Dropping missing countries

3.2. Calculating the number of cases for neighboring countries that month

3.3. Changing variable names, adding interactions

4. Results section for the paper

4.1. General table

4.2. Individualism score

4.2.1. Overall Individualism

4.2.2. Cumulative Individualism

4.2.3. Relationship between all variables

4.2.4. Relationship between government intervention and individualism

5. Running regressions

5.1. Regressions with total cases as of date

5.1.1. Getting interaction effects

5.1.2. Results with Tanzania

5.1.3. Results without Tanzania

5.2. Regression for different months

5.3. Regression for different seasons

5.3.1. Regression model summaries

5.3.2. Regression model summaries with robust standard errors and without Tanzania

5.3.3. Regression models with Tanzania

5.3.4. Without Tanzania

5.3.4.1. No Continents

5.3.4.2. Continents

5.3.5. Regression without an interaction effect

6. Diagnostics

6.1. Regression with total cases

6.1.1. Homoscedasticity of residuals + functional misspecification

6.1.1.1. Checking autumn data

6.1.1.2. Checking summer data

6.1.1.3. Diagnostics for all seasons

6.1.2. Multicollinearity

6.1.3. Homoscedasticity of residuals

6.1.4. Autocorrelation of residuals

6.1.5. Features and residuals are uncorrelated

6.1.6. Outliers

6.1.7. High leverage points

6.1.8. Normality of residuals

7. Additional Checks

7.1. Sensitivity check

7.2. Check on average government intervention

7.3. MCAR test

7.4. GDP Calculations

7.5. Stringency

7.6. Differences in COVID-19 rates and response

1. Extracting data

# Import wrangling packages
import os
import math
import pandas as pd
import numpy as np
import psycopg2
import itertools
import warnings
from scipy.stats import pearsonr
from difflib import SequenceMatcher
from datetime import datetime, timedelta
import re
import calendar

import statsmodels.formula.api as smf

# Import visualization packages
import matplotlib.pyplot as plt
import matplotlib.dates as mdates
import matplotlib.patches as mpatches
import matplotlib.style as style
import seaborn as sns
#import geopandas as gpd
#from shapely.geometry import Point, Polygon

1.1. Extracting indicators from the World Bank

# Establish connection

conn = psycopg2.connect(
    host='covid19db.org',
    port=5432,
    dbname='covid19',
    user='covid19',
    password='covid19')
cur = conn.cursor()

# Declaring which variables to use

vars_to_use = ['Population density (people per sq. km of land area)', 'Population ages 65 and above, total', 'Air transport, passengers carried', 'Current health expenditure (% of GDP)', 'GDP per capita (constant 2010 US$)', 'Population, total']

# Add quotation characters
quote = "\'"
vars_to_use2 = [quote + x + quote for x in vars_to_use]

# Get total number of cases

sql_command = f"""
SELECT country, indicator_name, value, year
FROM world_bank
WHERE indicator_name IN ({', '.join(vars_to_use2)}) AND source = 'World Bank'
""" 
indicators_wb = pd.read_sql(sql_command, conn)

for var in vars_to_use:
    print(f"\nVariable {var}")
    display(indicators_wb.loc[indicators_wb.indicator_name == var, 'year'].value_counts())

Variable Population density (people per sq. km of land area)

2018    206
2017      4
1960      2
2019      2
2011      1
Name: year, dtype: int64

Variable Population ages 65 and above, total

2019    192
1960     22
2011      1
Name: year, dtype: int64

Variable Air transport, passengers carried

2018    154
1960     30
2004      4
2009      4
2014      4
1991      3
2016      3
1998      2
1999      2
2000      2
2017      2
1992      1
1996      1
2001      1
2012      1
2015      1
Name: year, dtype: int64

Variable Current health expenditure (% of GDP)

2017    185
1960     27
2011      1
2012      1
2015      1
Name: year, dtype: int64

Variable GDP per capita (constant 2010 US$)

2019    177
2018     16
1960     10
2010      4
2017      4
2011      1
2013      1
2014      1
2015      1
Name: year, dtype: int64

Variable Population, total

2019    214
2011      1
Name: year, dtype: int64

indicator_years = {'Population density (people per sq. km of land area)': 2018,
                   'Population ages 65 and above, total': 2019,
                   'Air transport, passengers carried': 2018,
                   'Current health expenditure (% of GDP)': 2017,
                   'GDP per capita (constant 2010 US$)': 2019,
                   'Population, total': 2019}

for key, year in indicator_years.items():
    indicators_wb = indicators_wb[~((indicators_wb.indicator_name == key) & (indicators_wb.year != year))].copy()
    
indicators_wb.groupby(['indicator_name', 'year']).size()

indicator_name                                       year
Air transport, passengers carried                    2018    154
Current health expenditure (% of GDP)                2017    185
GDP per capita (constant 2010 US$)                   2019    177
Population ages 65 and above, total                  2019    192
Population density (people per sq. km of land area)  2018    206
Population, total                                    2019    214
dtype: int64

ipv = indicators_wb.pivot_table(index=['country'], columns=['indicator_name'], values='value').reset_index()
ipv['passengers_carried_by_population'] = ipv['Air transport, passengers carried'] / ipv['Population, total']
ipv['65_and_above_by_population'] = ipv['Population ages 65 and above, total'] / ipv['Population, total']

1.2. Merging metrics, cases, and hofstede index

1.2.1. Extracting case data

def get_cases(conn):
    """Get the dataframe of the cases and population
    
    Args:
        conn (connection): a connection to the OXCOVID-19 DB
        
    Returns:
        cases_df (dataframe): dataframe containing COVID-19 data
    """

    # Get total number of cases
    sql_command = """
    SELECT  ep.date,
            ep.country,
            ep.confirmed,
            ep.dead, 
            ep.countrycode,
            wb.country AS country_wb,
            wb.value AS population
    FROM epidemiology AS ep
    LEFT JOIN world_bank AS wb
        ON ep.countrycode = wb.countrycode
    WHERE ep.source = 'WRD_WHO'
            AND wb.indicator_name = 'Population, total'
            AND wb.year = 2019 -- Maximum year
            AND ep.date <= '2020-12-31' -- Making sure there are no cases from 2021
    """
    cases_df = pd.read_sql(sql_command, conn)

    # Check data quality
    assert (cases_df['country'] == cases_df['country_wb']).mean() == 1, 'Not all countries are identical. Re-check join key.'
    assert cases_df.isnull().values.any() == False, 'There are missing values'

    
    # Check countries that are not included
    sql_command2 = """
    SELECT DISTINCT country
    FROM epidemiology

    EXCEPT

    SELECT DISTINCT country
    FROM world_bank
        """

    excluded = pd.read_sql(sql_command2, conn)
    print(f"A total of {len(excluded)} entries are excluded from the initial dataset since they do not have data for Population.\n"
          f"These are: {', '.join(excluded['country'])}")
    
    return cases_df


def calculate_capita_metrics(cases_df):
    """Calculate key metrics later used in the analysis
    
    Args:
        cases_df (dataframe): dataframe containing COVID-19 data
        
    Returns:
        cases_df (dataframe): dataframe with additional metrics
    """
    cases_df['confirmed_per_100K'] = (cases_df['confirmed'] / cases_df['population']) * 100_000
    cases_df['dead_per_100K'] = (cases_df['dead'] / cases_df['population']) * 100_000
    cases_df['dead_per_cases'] = cases_df['dead'] / cases_df['confirmed']
    
    cases_df['date'] = pd.to_datetime(cases_df['date'])
    cases_df['month'] = cases_df['date'].dt.month
    
    return cases_df


def get_daily_growth(cases_df):
    """Calculate daily growth of cases from the number of cumulative cases
    
    Args:
        cases_df (dataframe): dataframe containing COVID-19 data.
        
    Returns:
        cases_df (dataframe): dataframe with COVID-19 case differences.
    """
    # Get unique country list
    countries = cases_df['country'].unique()
    
    # Sort the df (diff calculations only work if it is sorted by country and year)
    cases_df.sort_values(['country', 'date'], ascending = True, inplace = True)
    
    # Get daily growth (proportional and absolute)
    differences = {'new_cases_total': 'confirmed',
                   'new_cases_per_100K': 'confirmed_per_100K',
                   'new_deaths_total': 'dead'}
    
    for country in countries:
        for col, measure in differences.items():
            cases_df.loc[cases_df['country'] == country, col] =\
            cases_df.loc[cases_df['country'] == country, measure].diff().fillna(0)
        
    return cases_df


def get_newest_df(cases_df, time_lag=10):
    """Get the newest data for the query with available data
    
    Args:
        cases_df (dataframe): dataframe containing COVID-19 data.
        time_lag (int, optional): number of days to substract from today for extracting data.
        
    Returns:
        df_newest (dataframe): dataframe with newest data.
    """
    
    newest_date = (datetime.today() - timedelta(days=time_lag)).strftime('%Y-%m-%d') 

    df_newest = cases_df[cases_df['date'] == newest_date]
    
    # Check that no data is lost
    assert df_newest['country'].nunique() == len(df_newest), 'Countries are not unique'
    assert df_newest['country'].nunique() == cases_df['country'].nunique(), f'Not all countries have the date {newest_date}'
    
    return df_newest


def daily_growth_check(cases_df, drop_countries=True, drop_threshold=0.05):
    """Check whether the daily growth of COVID-19 cases is below zero. 

    Perform a check on the number of daily COVID-19 cases for each country and excludes
    countries with a high number of negative daily cases. The daily cases should never be
    negative. The methodology for determining whether to drop a country or not is as follows.
    
    1. Extracting the total number of negative growth cases for each country
    2. Comparing the total number of negative growth cases to the overall cases in the country
    3. If the proportion of these is smaller than the threshold, the negative drop is deemed to be
    insigifnicant. Otherwise, the country is removed
    
    Example: Oxlandia had a cumulative number of 40,000 and 39,900 cases on September 1st and 2nd, respectively.
    Oxlandia currently has a total of 100 thousand cummulative cases. Since the drop was 100 cases, it is only 0.1%
    of if its current cases. If the drop is less than the threshold, Oxlandia is not removed.
    
    Args:
        cases_df (dataframe): dataframe containing COVID-19 data.
        drop_countries (boolean): indicate whether to drop countries or not.
        drop_threshold (float): the threshold beow which countries are dropped.
        
    Returns
        cases_df (dataframe): new dataframe without the countries that have overall drops above the specified threshold.
    """
    
    
    # Check if there are negative cases
    negative_diff = np.sum(cases_df['new_cases_total'] < 0)
    if negative_diff > 0:
        print(f"\nThere are {negative_diff} cases of negative daily growth in cases from the data\n")
        
        # Get the drops for all the countries
        negative_df = cases_df[cases_df['new_cases_total'] < 0].copy()
        all_drops = negative_df.groupby('country').new_cases_total.sum()
        
        if drop_countries:
            # Calculate the countries with a drop above the threshold
            df_newest = get_newest_df(cases_df)
            drop_countries = []
            for country in all_drops.index:
                total_cases = df_newest.loc[df_newest['country'] == country, 'confirmed']
                perc_drop =  - (all_drops[country]/total_cases).values
                if perc_drop > drop_threshold:
                    drop_countries.append(country)

            if len(drop_countries) > 0:
                print("Dropped {} countries from further analysis: {}.\n".format(len(drop_countries), ', '.join(drop_countries)))
                cases_df = cases_df[~cases_df['country'].isin(drop_countries)]            

        return cases_df

cases_df = get_cases(conn)
cases_df = calculate_capita_metrics(cases_df)
cases_df = get_daily_growth(cases_df) 
cases_df = daily_growth_check(cases_df, drop_countries = True)

A total of 30 entries are excluded from the initial dataset since they do not have data for Population.
These are: Mayotte, Other continent, Saint Helena, Oceania, Pitcairn Islands, Martinique, Reunion, Wallis and Futuna, Guernsey, Montserrat, Cook Islands, Kosovo, Asia, French Guiana, Bonaire, Sint Eustatius and Saba, Tokelau, Saint-Barthélemy, America, Saint Pierre and Miquelon, Falkland Islands, Taiwan, Niue, Anguilla, World, Guadeloupe, Africa, Western Sahara, Vatican City, Europe, Jersey

There are 64 cases of negative daily growth in cases from the data

Dropped 4 countries from further analysis: Benin, Ecuador, Puerto Rico, São Tomé and Príncipe.

def get_metrics_df(df):
    df['month'] = df['date'].map(lambda x: pd.to_datetime(x).month)    
    return df
cases_df = get_metrics_df(cases_df)

1.2.2. Hofstede index

cultural_df = pd.read_excel("6-dimensions-for-website-2015-08-16.xls")

# Get country estimates
cultural_df['country'] = cultural_df['country'].map(lambda x: x[:-3] + 'Republic' if str(x)[-3:] == 'Rep' else x)

print("Estimated: ", cultural_df[cultural_df['idv'].notnull()]['Estimated'].sum())

change_names = {'Bosnia': 'Bosnia and Herzegovina',
                'Great Britain' : 'United Kingdom',
                'Kyrgyz Republic': 'Kyrgyzstan',
                'Macedonia Republic': 'Macedonia',
                'Slovak Republic': 'Slovakia',
                'U.S.A.': 'United States',
                'Korea South': 'South Korea'}

cultural_df['country'] = cultural_df['country'].replace(change_names)

Estimated:  24.0

df_cult_cases = cultural_df.merge(cases_df, how = 'left', left_on = 'country', right_on = 'country', validate='one_to_many')
cultural_set = set(cultural_df['country'].unique())
cases_set = set(cases_df['country'])
cultural_set.difference(cases_set)

{'Africa East',
 'Africa West',
 'Arab countries',
 'Belgium French',
 'Belgium Netherl',
 'Canada French',
 'Ecuador',
 'Germany East',
 'Hong Kong',
 'Puerto Rico',
 'South Africa white',
 'Switzerland French',
 'Switzerland German',
 'Taiwan'}

df1 = df_cult_cases.merge(ipv, how= 'left', left_on='country', right_on='country', validate='many_to_one')

ipv_countries = set(ipv['country'].unique())
df1_countries = set(df1['country'].unique())
df1_countries.difference(ipv_countries)

{'Africa East',
 'Africa West',
 'Arab countries',
 'Belgium French',
 'Belgium Netherl',
 'Canada French',
 'Germany East',
 'South Africa white',
 'Switzerland French',
 'Switzerland German',
 'Taiwan'}

def c_count(df):
    print("Unique countries:", df['country'].nunique())

c_count(df1)
c_count(cultural_df)
c_count(df_cult_cases)

Unique countries: 111
Unique countries: 111
Unique countries: 111

1.2.3. Merging the data

df1['month'] = pd.to_datetime(df1.date).dt.month
df1_agg = df1.groupby(['country', 'month']).agg({ 'idv': 'mean',
                                        'confirmed': 'max', # latest # of cumulative cases each month
                                        'dead': 'max', # latest dead cases of each month
                                        'population': 'mean',
                                        'Current health expenditure (% of GDP)': 'mean',
                                        'passengers_carried_by_population': 'mean',
                                        'GDP per capita (constant 2010 US$)': 'mean',
                                        'Population ages 65 and above, total': 'mean',
                                        'Population density (people per sq. km of land area)': 'mean',
                                        '65_and_above_by_population': 'mean',
                                        'Population, total': 'mean',
                                        'new_cases_per_100K': 'sum',
                                        'new_cases_total': 'sum',
                                        'new_deaths_total': 'sum'}).reset_index() 

def get_logs(df, vars_to_log=['new_cases_total', 'new_cases_per_100K', 'new_deaths_total']):
    
    for var in vars_to_log:
        df[var + '_log'] = np.log(df[var] + 0.000001)
        
    return df

df1_agg = get_logs(df1_agg)
ipv_countries = set(df1['country'].unique())
df1_countries = set(df1_agg['country'].unique())
ipv_countries.difference(df1_countries)

{'Africa East',
 'Africa West',
 'Arab countries',
 'Belgium French',
 'Belgium Netherl',
 'Canada French',
 'Ecuador',
 'Germany East',
 'Hong Kong',
 'Puerto Rico',
 'South Africa white',
 'Switzerland French',
 'Switzerland German',
 'Taiwan'}

df1_countries.difference(ipv_countries)

set()

c_count(df1_agg)

Unique countries: 97

1.3. Mobility data

1.3.1. Extracting the data

mobility = pd.read_csv("Global_Mobility_Report.csv")
mob = mobility[['country_region', 'date', 'retail_and_recreation_percent_change_from_baseline', 'parks_percent_change_from_baseline', 'transit_stations_percent_change_from_baseline', 'workplaces_percent_change_from_baseline']].copy()
mob['month'] = pd.to_datetime(mob['date']).dt.month # get month
mob_agg_all = mob.groupby(['country_region', 'month']).mean()#.reset_index() # group by baseline
mob_agg = mob_agg_all.mean(axis=1).reset_index().rename(columns={0:'mobility_index'})

C:\Users\Paulius\AppData\Roaming\Python\Python38\site-packages\IPython\core\interactiveshell.py:3146: DtypeWarning: Columns (4,5) have mixed types.Specify dtype option on import or set low_memory=False.
  has_raised = await self.run_ast_nodes(code_ast.body, cell_name,

df2_agg = df1_agg.merge(mob_agg, how = 'left', left_on = ['country', 'month'], right_on = ['country_region', 'month'], validate = 'one_to_one')
df2_agg['country'].nunique()

97

# Drop month 1
df2_agg = df2_agg[df2_agg['month'] != 1].copy()

1.3.2. Plotting mobility data

fig, axs = plt.subplots(5,2, figsize = (30,15))

ax_list = [item for sublist in axs for item in sublist]

for country in mob['country_region'].unique()[0:10]:
    ax = ax_list.pop(0)
    df_ = mob[mob['country_region'] == country]
    sns.scatterplot(x = 'date', y = 'retail_and_recreation_percent_change_from_baseline', data = df_, ax=ax)
    ax.set_title(country)
    ax.set_xlabel('')
    ax.set_ylabel('')

1.4. Testing data

cols = ['location', 'date', 'new_tests']
tests_df = pd.read_csv("owid-covid-data.csv")[cols]

tests_df = tests_df.fillna(-1) # to get where there is NA

tests_df['month'] = pd.to_datetime(tests_df.date).dt.month 
tests_df_agg = tests_df.groupby(['month', 'location']).agg({'new_tests': ['sum', 'min']}
                                                          ).reset_index().sort_values(['location', 'month'])

tests_df_agg = pd.concat([tests_df_agg[['month', 'location']], tests_df_agg['new_tests']], axis = 1)
tests_df_agg.columns = ['month', 'location', 'sum_new_tests', 'min_new_tests'] # Get where is NA by looking at where min_new_tests == -1

df3_agg = df2_agg.merge(tests_df_agg, how = 'left', left_on = ['country', 'month'], right_on = ['location', 'month'], validate='one_to_one').drop('location', axis = 1)
df3_agg

1.5. Governmental response

# Get total number of cases
sql_command = """
SELECT containment_health_index, date, country
FROM government_response

"""
gov_df = pd.read_sql(sql_command, conn)

def group_month(df, var, country_var='country'):
    df['month'] = pd.to_datetime(df.date).dt.month 
    df_agg = df.groupby(['month', country_var]).agg({var: 'mean'}).reset_index().sort_values(['country', 'month'])
    
    return df_agg

gov_df_agg = group_month(gov_df, 'containment_health_index')

df4_agg = df3_agg.merge(gov_df_agg, how = 'left', left_on = ['country', 'month'], right_on = ['country', 'month'], validate='one_to_one')

1.6. Regime Type

economist_df = pd.read_excel("The_Economist.xlsx")
economist_df = economist_df.loc[economist_df['time'] == 2019, ['name', 'Democracy index (EIU)']].copy()
economist_df.columns = ['country', 'democracy_index']
df5_agg = df4_agg.merge(economist_df, how = 'left', left_on = ['country'], right_on = ['country'], validate='many_to_one')

1.7. Distance from Wuhan

from opencage.geocoder import OpenCageGeocode
from geopy.distance import geodesic
from countryinfo import CountryInfo
import apikeys # Manual file
import pycountry_convert as pc

key = apikeys['key']  # Get the key
geocoder = OpenCageGeocode(key)

from functools import lru_cache

capitals = {'Slovakia': 'Bratislava',
 'Slovenia': 'Ljubljana',
 'South Africa': 'Cape Town',
 'South Korea': 'Seoul', 
 'Spain': 'Madrid',
 'Sweden': 'Stockholm',
 'Switzerland': 'Bern',
 'Tanzania': 'Dodoma',
 'Thailand': 'Bangkok',
 'Trinidad and Tobago': 'Port of Spain',
 'Turkey': 'Ankara',
 'Uganda': 'Kampala',
 'Ukraine': 'Kyiv', 
 'United Kingdom': 'London',
 'United States': 'Washington, D.C.',
 'Uruguay': 'Montevideo',
 'Venezuela': 'Caracas',
 'Vietnam': 'Hanoi',
 'Zambia': 'Lusaka',
 'Zimbabwe': 'Harare'}

capitals_2 = {
    'Andorra': 'Andorra la Vella',
    'Macedonia': 'Skopje',
    'Montenegro': 'Podgorica'
}

@lru_cache(maxsize=100)
def get_capital(country, capitals_2=capitals_2):
    
    if country in capitals_2.keys():
        return capitals_2[country]
    try:
    # Get the capital
        capital = CountryInfo(country).capital()
        return capital
    except:
        return None

df5_agg['capital'] = df5_agg['country'].map(get_capital)
df5_agg[df5_agg['capital'].map(lambda x: x is None)]['country'].unique()
lat_B, lng_B = geocoder.geocode('Wuhan')[0]['geometry'].values()

array([], dtype=object)

@lru_cache(maxsize=100)
def find_distance(city, lat_B=lat_B, lng_B=lng_B):
    
    result_A = geocoder.geocode(city)

    # Get lat, long
    lat_A, lng_A = result_A[0]['geometry'].values()
    
    return geodesic((lat_A,lng_A), (lat_B,lng_B)).km

df5_agg['distance'] = df5_agg['capital'].map(find_distance)

c_count(df5_agg)

Unique countries: 97

def get_continent(name):
    country_code = pc.country_name_to_country_alpha2(name, cn_name_format="default")
    continent_name = pc.country_alpha2_to_continent_code(country_code)
    return continent_name

def c_count(df):
    print("Unique countries:", df['country'].nunique())

df5_agg['continent'] = df5_agg.country.map(get_continent)
df5_agg['confirmed_log'] = np.log(df5_agg['confirmed'] + 0.0000000000001)

df5_agg.columns = [re.sub(r'[^\w]', '', x.replace(' ', '_')).lower() for x in df5_agg.columns] # Change col names
df5_agg.rename(columns={'current_health_expenditure__of_gdp': 'current_health_expenditure_of_gdp',
                       '65_and_above_by_population': 'over65_per_capita'}, inplace=True)
df5_agg.to_csv("2021-01-04 stats_dataset.csv", index=False)

2. COVID-19 and Individualism EDA

from scipy.stats import pearsonr

df = pd.read_csv("2021-01-04 stats_dataset.csv")

2.1. Getting COVID-19 data per month

def get_individualism_scores(df=df, remove_last_plot=True):

    fig, axs = plt.subplots(4,3, figsize = (18,12))

    ax_list = [item for sublist in axs for item in sublist]

    for month in range(2,13):
        ax = ax_list.pop(0)
        df_ = df[df['month'] == month]
        df_ = df_[df_['new_cases_per_100k'] != 0]
        df_ = df_[df_['individualism_index'].notnull()]
        sns.regplot(x = 'new_cases_per_100k_log', y = 'individualism_index', data = df_, ax=ax)
        corr, p = pearsonr(df_['new_cases_per_100k_log'], df_['individualism_index'])
        ax.set_title(f"Month: {month}, R^2: {corr.round(2)}, p = {p.round(3)}")
        
        ax.set_ylim([0,100])

        # Set X labels
        if month in (1,4,7,10): ax.set_ylabel("Individualism score")
        else: ax.set_ylabel("")

        if month in (10,11,12): ax.set_xlabel("New cases per 100K people, log")
        else: ax.set_xlabel("")

    
    if remove_last_plot:
        fig.delaxes(axs[3,2])
    fig.suptitle("Relationship between individualism and new monthly COVID-19 cases", fontsize = 16)
    plt.tight_layout()
    plt.subplots_adjust(top=0.9)

get_individualism_scores()

df_ = df[df['month'] == month]
df_ = df_[df_['new_cases_per_100k'] != 0]
df_ = df_[df_['individualism_index'].notnull()]
sns.regplot(x = 'new_cases_per_100k_log', y = 'individualism_index', data = df_)
sns.regplot(x = 'new_cases_per_100k_log', y = 'individualism_index', data = df_[~df_.country.isin(['Australia', 'New Zealand', 'Vietnam'])])

<AxesSubplot:xlabel='new_cases_per_100k_log', ylabel='individualism_index'>

df_2 = df_[~df_.country.isin(['Australia', 'New Zealand', 'Vietnam'])].copy()
corr, p = pearsonr(df_2['new_cases_per_100k_log'], df_2['individualism_index'])

corr

0.5207701239060172

fig, axs = plt.subplots(4,3, figsize = (17,12))

ax_list = [item for sublist in axs for item in sublist]

for month in range(2,13):
    ax = ax_list.pop(0)
    df_ = df[df['month'] == month]
    df_ = df_[df_['new_cases_per_100k'] != 0]
    sns.regplot(x = 'confirmed_log', y = 'idv', data = df_, ax=ax)
    ax.set_title(f"Month: {month}")
    
plt.tight_layout()

2.2. Getting COVID-19 data by month for a number of countries

countries_unique = df['country'].unique()

fig, axs = plt.subplots(10,10, figsize=(5*10,4*9), sharex=True, sharey=True)
ax_list = [item for sublist in axs for item in sublist]

for country in countries_unique:
    ax = ax_list.pop(0)
    df_ = df[df['country'] == country]
    sns.scatterplot(x='month', y = 'new_cases_per_100k_log', data = df_, ax = ax)
    ax.set_title(country)

plt.tight_layout()

3. Cleaning the data

3.1. Dropping missing countries

drop_c = df.loc[df.idv.isnull(),'country'].unique()
print(f"Dropping {drop_c} countries due to missing values with the dependent variable")
df = df[~df['country'].isin(drop_c)].copy()

Dropping ['Andorra' 'Cyprus' 'Kyrgyzstan' 'Macedonia' 'Mali' 'Rwanda' 'Uganda'
 'Zimbabwe'] countries due to missing values with the dependent variable

c_count(df)

Unique countries: 89

null_cols = df.columns[~df.notnull().all()]

df[null_cols].isnull().sum()

current_health_expenditure_of_gdp                    22
passengers_carried_by_population                     88
gdp_per_capita_constant_2010_us                      22
population_density_people_per_sq_km_of_land_area     22
country_region                                      123
mobility_index                                      123
sum_new_tests                                        44
min_new_tests                                        44
containment_health_index                             23
democracy_index                                      11
continent                                           110
dtype: int64

for col in null_cols:
    countries = df.loc[df[col].isnull(),'country'].unique()
    print(f"Column: {col}. Countries missing: {countries}")

Column: current_health_expenditure_of_gdp. Countries missing: ['Albania' 'Montenegro']
Column: passengers_carried_by_population. Countries missing: ['Armenia' 'Bosnia and Herzegovina' 'Denmark' 'Dominican Republic'
 'Norway' 'Slovakia' 'Sweden' 'Uruguay']
Column: gdp_per_capita_constant_2010_us. Countries missing: ['Iran' 'Venezuela']
Column: population_density_people_per_sq_km_of_land_area. Countries missing: ['Georgia' 'Moldova']
Column: country_region. Countries missing: ['Albania' 'Algeria' 'Armenia' 'Azerbaijan' 'China' 'Czech Republic'
 'Ethiopia' 'Georgia' 'Iceland' 'Iran' 'Montenegro' 'Serbia' 'Suriname']
Column: mobility_index. Countries missing: ['Albania' 'Algeria' 'Armenia' 'Azerbaijan' 'China' 'Czech Republic'
 'Ethiopia' 'Georgia' 'Iceland' 'Iran' 'Montenegro' 'Serbia' 'Suriname']
Column: sum_new_tests. Countries missing: ['Albania' 'Armenia' 'Azerbaijan' 'Bangladesh' 'Bosnia and Herzegovina'
 'Bulgaria' 'Burkina Faso' 'Colombia' 'Costa Rica' 'Czech Republic'
 'Dominican Republic' 'El Salvador' 'Ethiopia' 'Ghana' 'Hungary'
 'Indonesia' 'Jamaica' 'Jordan' 'Moldova' 'Montenegro' 'Panama' 'Peru'
 'Poland' 'Saudi Arabia' 'Slovakia' 'Slovenia' 'Suriname' 'Tanzania'
 'Trinidad and Tobago' 'Turkey' 'Ukraine' 'Uruguay' 'Venezuela' 'Zambia']
Column: min_new_tests. Countries missing: ['Albania' 'Armenia' 'Azerbaijan' 'Bangladesh' 'Bosnia and Herzegovina'
 'Bulgaria' 'Burkina Faso' 'Colombia' 'Costa Rica' 'Czech Republic'
 'Dominican Republic' 'El Salvador' 'Ethiopia' 'Ghana' 'Hungary'
 'Indonesia' 'Jamaica' 'Jordan' 'Moldova' 'Montenegro' 'Panama' 'Peru'
 'Poland' 'Saudi Arabia' 'Slovakia' 'Slovenia' 'Suriname' 'Tanzania'
 'Trinidad and Tobago' 'Turkey' 'Ukraine' 'Uruguay' 'Venezuela' 'Zambia']
Column: containment_health_index. Countries missing: ['Armenia' 'Montenegro' 'Netherlands']
Column: democracy_index. Countries missing: ['Slovakia']
Column: continent. Countries missing: ['Canada' 'Costa Rica' 'Dominican Republic' 'El Salvador' 'Guatemala'
 'Jamaica' 'Mexico' 'Panama' 'Trinidad and Tobago' 'United States']

countries_drop = ['Albania', 'Montenegro', 'Puerto Rico', 'Iran', 'Venezuela', 'Armenia', 'Montenegro', 'Netherlands', 'Slovakia']
df = df[~df.country.isin(countries_drop)].copy()

for col in null_cols:
    countries = df.loc[df[col].isnull(),'country'].unique()
    print(f"Column: {col}. Countries missing: {countries}")

Column: current_health_expenditure_of_gdp. Countries missing: []
Column: passengers_carried_by_population. Countries missing: ['Bosnia and Herzegovina' 'Denmark' 'Dominican Republic' 'Norway' 'Sweden'
 'Uruguay']
Column: gdp_per_capita_constant_2010_us. Countries missing: []
Column: population_density_people_per_sq_km_of_land_area. Countries missing: ['Georgia' 'Moldova']
Column: country_region. Countries missing: ['Algeria' 'Azerbaijan' 'China' 'Czech Republic' 'Ethiopia' 'Georgia'
 'Iceland' 'Serbia' 'Suriname']
Column: mobility_index. Countries missing: ['Algeria' 'Azerbaijan' 'China' 'Czech Republic' 'Ethiopia' 'Georgia'
 'Iceland' 'Serbia' 'Suriname']
Column: sum_new_tests. Countries missing: ['Azerbaijan' 'Bangladesh' 'Bosnia and Herzegovina' 'Bulgaria'
 'Burkina Faso' 'Colombia' 'Costa Rica' 'Czech Republic'
 'Dominican Republic' 'El Salvador' 'Ethiopia' 'Ghana' 'Hungary'
 'Indonesia' 'Jamaica' 'Jordan' 'Moldova' 'Panama' 'Peru' 'Poland'
 'Saudi Arabia' 'Slovenia' 'Suriname' 'Tanzania' 'Trinidad and Tobago'
 'Turkey' 'Ukraine' 'Uruguay' 'Zambia']
Column: min_new_tests. Countries missing: ['Azerbaijan' 'Bangladesh' 'Bosnia and Herzegovina' 'Bulgaria'
 'Burkina Faso' 'Colombia' 'Costa Rica' 'Czech Republic'
 'Dominican Republic' 'El Salvador' 'Ethiopia' 'Ghana' 'Hungary'
 'Indonesia' 'Jamaica' 'Jordan' 'Moldova' 'Panama' 'Peru' 'Poland'
 'Saudi Arabia' 'Slovenia' 'Suriname' 'Tanzania' 'Trinidad and Tobago'
 'Turkey' 'Ukraine' 'Uruguay' 'Zambia']
Column: containment_health_index. Countries missing: []
Column: democracy_index. Countries missing: []
Column: continent. Countries missing: ['Canada' 'Costa Rica' 'Dominican Republic' 'El Salvador' 'Guatemala'
 'Jamaica' 'Mexico' 'Panama' 'Trinidad and Tobago' 'United States']

exclude_cols = ['sum_new_tests', 'min_new_tests', 'passengers_carried_by_population', 'country_region']
df = df.drop(exclude_cols, axis = 1).copy()

df['continent'].isnull().sum()

110

df['continent'] = df['continent'].map(lambda x: 'N.A.' if pd.isnull(x)  else 'SA' if x == 'Trinidad and Tobago' else x)
for col in df.columns[~df.notnull().all()]:
    countries = df.loc[df[col].isnull(),'country'].unique()
    print(f"Column: {col}. Countries missing: {countries}")

Column: population_density_people_per_sq_km_of_land_area. Countries missing: ['Georgia' 'Moldova']
Column: mobility_index. Countries missing: ['Algeria' 'Azerbaijan' 'China' 'Czech Republic' 'Ethiopia' 'Georgia'
 'Iceland' 'Serbia' 'Suriname']

df = df[~df.country.isin(['Moldova', 'Georgia'])].copy()

for col in df.columns[~df.notnull().all()]:
    countries = df.loc[df[col].isnull(),'country'].unique()
    print(f"Column: {col}. Countries missing: {countries}")

Column: mobility_index. Countries missing: ['Algeria' 'Azerbaijan' 'China' 'Czech Republic' 'Ethiopia' 'Iceland'
 'Serbia' 'Suriname']

drop_countries = ['Algeria', 'Azerbaijan', 'China', 'Czech Republic', 'Ethiopia', 'Iceland', 'Serbia', 'Suriname']
df = df[~df.country.isin(drop_countries)].copy()

for col in df.columns[~df.notnull().all()]:
    countries = df.loc[df[col].isnull(),'country'].unique()
    print(f"Column: {col}. Countries missing: {countries}")

3.2. Calculating the number of cases for neighboring countries that month

from countryinfo import CountryInfo
import pycountry

cases_df = get_cases(conn)
cases_df = calculate_capita_metrics(cases_df)
cases_df = get_daily_growth(cases_df) 
cases_df = daily_growth_check(cases_df, drop_countries = True)

A total of 30 entries are excluded from the initial dataset since they do not have data for Population.
These are: Mayotte, Other continent, Saint Helena, Oceania, Pitcairn Islands, Martinique, Reunion, Wallis and Futuna, Guernsey, Montserrat, Cook Islands, Kosovo, Asia, French Guiana, Bonaire, Sint Eustatius and Saba, Tokelau, Saint-Barthélemy, America, Saint Pierre and Miquelon, Falkland Islands, Taiwan, Niue, Anguilla, World, Guadeloupe, Africa, Western Sahara, Vatican City, Europe, Jersey

There are 64 cases of negative daily growth in cases from the data

Dropped 4 countries from further analysis: Benin, Ecuador, Puerto Rico, São Tomé and Príncipe.

def get_month_agg(df):
    df['month'] = pd.to_datetime(df.date).dt.month
    df1_agg = df.groupby(['country', 'month']).agg({
                                            'confirmed': 'max', # latest # of cumulative cases each month
                                            'new_cases_per_100K': 'sum'}).reset_index() 
    
    return df1_agg

cases_df = get_month_agg(cases_df)

def get_neighbors_all(df):
        
    countries_correct = {'Albania': ['MNE', 'GRC', 'MKD'],
                         'Serbia': ['HUN', 'ROU', 'BGR', 'MKD', 'HRV', 'BIH', 'MNE', 'ALB'],
                         'South Korea': []}
    
    change_names = {'Russian Federation': 'Russia',
                    'Iran, Islamic Republic of': 'Iran',
                    'Bolivia, Plurinational State of': 'Bolivia',
                    'Czechia': 'Czech Republic',
                    'Tanzania, United Republic of': 'Tanzania',
                     'Viet Nam': 'Vietnam'
                    }
    for country in df.country.unique():

        print(f"Country: {country}")
        # Get neighbors (short names)
        try:
            countries_short = CountryInfo(country).borders()
        except KeyError:
            print(f"Passing country {country}")
            continue
        
        # Add corrections due to package problems
        if country in countries_correct.keys():
            countries_short = countries_correct[country]
            

        # Get full list of countries
        get_name = lambda x: pycountry.countries.get(alpha_3=x).name
        bordering_countries = list(map(get_name, countries_short))
        bordering_countries = [change_names[x] if x in change_names.keys() else x for x in bordering_countries]

            # Get country average cases for the country
        unique_after = df[df.country.isin(bordering_countries)].country.unique()

        if len(unique_after) != len(bordering_countries):
            set_diff = set(bordering_countries).difference(set(unique_after))
            print(f"Country {country} missing: {set_diff}")
        
        country_avg_cases = df.loc[df.country.isin(bordering_countries)].groupby(['month']).new_cases_per_100K.mean().reset_index()
        

        # Check if there are any borders
        if len(bordering_countries) == 0:
            continue

        # Get country average cases for the country
        country_avg_cases = df.loc[df.country.isin(bordering_countries)].groupby(['month']).new_cases_per_100K.mean().reset_index()

        # Get the indices for the main country (required to assign series to df)
        indices = df.loc[(df.country == country)].index
        values_to_set = country_avg_cases.set_index(indices)['new_cases_per_100K']

        # Set the dataframe values
        df.loc[(df.country == country), 'cases_neighbors'] = values_to_set
        
    return df

cases_df = get_neighbors_all(cases_df)

Country: Afghanistan
Country: Albania
Country Albania missing: {'North Macedonia'}
Country: Algeria
Country Algeria missing: {'Western Sahara'}
Country: American Samoa
Country: Andorra
Passing country Andorra
Country: Angola
Country Angola missing: {'Congo, The Democratic Republic of the', 'Namibia', 'Congo'}
Country: Antigua and Barbuda
Country: Argentina
Country: Armenia
Country: Aruba
Country: Australia
Country: Austria
Country: Azerbaijan
Country: Bahamas
Passing country Bahamas
Country: Bahrain
Country: Bangladesh
Country: Barbados
Country: Belarus
Country: Belgium
Country: Belize
Country: Bermuda
Country: Bhutan
Country: Bolivia
Country: Bosnia and Herzegovina
Country: Botswana
Country Botswana missing: {'Namibia'}
Country: Brazil
Country Brazil missing: {'French Guiana', 'Venezuela, Bolivarian Republic of'}
Country: British Virgin Islands
Passing country British Virgin Islands
Country: Brunei
Country: Bulgaria
Country Bulgaria missing: {'North Macedonia'}
Country: Burkina Faso
Country Burkina Faso missing: {'Benin'}
Country: Burundi
Country Burundi missing: {'Congo, The Democratic Republic of the'}
Country: Cambodia
Country Cambodia missing: {"Lao People's Democratic Republic"}
Country: Cameroon
Country Cameroon missing: {'Congo'}
Country: Canada
Country: Cape Verde
Country: Cayman Islands
Country: Central African Republic
Country Central African Republic missing: {'Congo, The Democratic Republic of the', 'Congo'}
Country: Chad
Country: Chile
Country: China
Country China missing: {"Lao People's Democratic Republic", 'Hong Kong', "Korea, Democratic People's Republic of", 'Macao'}
Country: Colombia
Country Colombia missing: {'Ecuador', 'Venezuela, Bolivarian Republic of'}
Country: Comoros
Country: Costa Rica
Country: Croatia
Country: Cuba
Country: Cyprus
Country: Czech Republic
Country: Côte d'Ivoire
Passing country Côte d'Ivoire
Country: Democratic Republic of the Congo
Country Democratic Republic of the Congo missing: {'Congo'}
Country: Denmark
Country: Djibouti
Country Djibouti missing: {'Eritrea'}
Country: Dominica
Country: Dominican Republic
Country: Egypt
Country: El Salvador
Country: Equatorial Guinea
Country: Estonia
Country: Ethiopia
Country Ethiopia missing: {'Eritrea'}
Country: Faroe Islands
Country: Fiji
Country: Finland
Country: France
Country: French Polynesia
Country: Gabon
Country Gabon missing: {'Congo'}
Country: Gambia
Passing country Gambia
Country: Georgia
Country: Germany
Country: Ghana
Country: Gibraltar
Country: Greece
Country Greece missing: {'North Macedonia'}
Country: Greenland
Country: Grenada
Country: Guam
Country: Guatemala
Country: Guinea
Country: Guinea-Bissau
Country: Guyana
Country Guyana missing: {'Venezuela, Bolivarian Republic of'}
Country: Haiti
Country: Honduras
Country: Hungary
Country: Iceland
Country: India
Country: Indonesia
Country: Iran
Country: Iraq
Country Iraq missing: {'Syrian Arab Republic'}
Country: Ireland
Country: Isle of Man
Country: Israel
Country Israel missing: {'Syrian Arab Republic'}
Country: Italy
Country Italy missing: {'Holy See (Vatican City State)'}
Country: Jamaica
Country: Japan
Country: Jordan
Country Jordan missing: {'Syrian Arab Republic'}
Country: Kazakhstan
Country: Kenya
Country: Kiribati
Country: Kuwait
Country: Kyrgyzstan
Country: Laos
Country: Latvia
Country: Lebanon
Country Lebanon missing: {'Syrian Arab Republic'}
Country: Lesotho
Country: Liberia
Country: Libya
Country: Liechtenstein
Country: Lithuania
Country: Luxembourg
Country: Macedonia
Passing country Macedonia
Country: Madagascar
Country: Malawi
Country: Malaysia
Country Malaysia missing: {'Brunei Darussalam'}
Country: Maldives
Country: Mali
Country: Malta
Country: Marshall Islands
Country: Mauritania
Country Mauritania missing: {'Western Sahara'}
Country: Mauritius
Country: Mexico
Country: Micronesia
Passing country Micronesia
Country: Moldova
Country: Monaco
Country: Mongolia
Country: Montenegro
Passing country Montenegro
Country: Morocco
Country Morocco missing: {'Western Sahara'}
Country: Mozambique
Country Mozambique missing: {'Eswatini'}
Country: Myanmar
Passing country Myanmar
Country: Nauru
Country: Nepal
Country: Netherlands
Country: New Caledonia
Country: New Zealand
Country: Nicaragua
Country: Niger
Country Niger missing: {'Benin'}
Country: Nigeria
Country Nigeria missing: {'Benin'}
Country: North Korea
Country North Korea missing: {'Korea, Republic of'}
Country: Northern Mariana Islands
Country: Norway
Country: Oman
Country: Pakistan
Country: Palau
Country: Palestina
Passing country Palestina
Country: Panama
Country: Papua New Guinea
Country: Paraguay
Country: Peru
Country Peru missing: {'Ecuador'}
Country: Philippines
Country: Poland
Country: Portugal
Country: Qatar
Country: Republic of Congo
Passing country Republic of Congo
Country: Romania
Country Romania missing: {'Moldova, Republic of'}
Country: Russia
Country Russia missing: {"Korea, Democratic People's Republic of"}
Country: Rwanda
Country Rwanda missing: {'Congo, The Democratic Republic of the'}
Country: Saint Kitts and Nevis
Country: Saint Lucia
Country: Saint Vincent and the Grenadines
Country: Saint-Martin
Passing country Saint-Martin
Country: Samoa
Country: San Marino
Country: Saudi Arabia
Country: Senegal
Country: Serbia
Country Serbia missing: {'North Macedonia'}
Country: Seychelles
Country: Sierra Leone
Country: Singapore
Country: Slovakia
Country: Slovenia
Country: Solomon Islands
Country: Somalia
Country: South Africa
Country South Africa missing: {'Eswatini', 'Namibia'}
Country: South Korea
Country: South Sudan
Country South Sudan missing: {'Congo, The Democratic Republic of the'}
Country: Spain
Country: Sri Lanka
Country: Sudan
Country Sudan missing: {'Eritrea'}
Country: Suriname
Country Suriname missing: {'French Guiana'}
Country: Swaziland
Country: Sweden
Country: Switzerland
Country: Syria
Country: Tajikistan
Country: Tanzania
Country Tanzania missing: {'Congo, The Democratic Republic of the'}
Country: Thailand
Country Thailand missing: {"Lao People's Democratic Republic"}
Country: Timor-Leste
Passing country Timor-Leste
Country: Togo
Country Togo missing: {'Benin'}
Country: Tonga
Country: Trinidad and Tobago
Country: Tunisia
Country: Turkey
Country Turkey missing: {'Syrian Arab Republic'}
Country: Turkmenistan
Country: Turks and Caicos Islands
Passing country Turks and Caicos Islands
Country: Tuvalu
Country: Uganda
Country Uganda missing: {'Congo, The Democratic Republic of the'}
Country: Ukraine
Country Ukraine missing: {'Moldova, Republic of'}
Country: United Arab Emirates
Country: United Kingdom
Country: United States
Country: Uruguay
Country: Uzbekistan
Country: Vanuatu
Country: Venezuela
Country: Vietnam
Country Vietnam missing: {"Lao People's Democratic Republic"}
Country: Virgin Islands, U.S.
Passing country Virgin Islands, U.S.
Country: Yemen
Country: Zambia
Country Zambia missing: {'Congo, The Democratic Republic of the', 'Namibia'}
Country: Zimbabwe

cases_df[cases_df.country.isin(['Russia', 'Belarus', 'Latvia', 'Poland']) & (cases_df.month == 6)]['new_cases_per_100K'].mean()

102.71813229329884

cases_df[cases_df.country == 'Lithuania']

	country	month	confirmed	new_cases_per_100K	cases_neighbors
1248	Lithuania	1	146637	217.378511	81.953512
1249	Lithuania	2	1	0.035883	0.002641
1250	Lithuania	3	484	17.331433	7.070394
1251	Lithuania	4	1449	31.971650	65.594832
1252	Lithuania	5	1670	10.585451	137.057066
1253	Lithuania	6	1816	5.238901	102.718132
1254	Lithuania	7	2062	8.827189	57.774407
1255	Lithuania	8	2874	29.136902	53.677582
1256	Lithuania	9	4578	61.144434	68.289774
1257	Lithuania	10	13823	331.737263	344.114493
1258	Lithuania	11	61325	1704.508756	788.182962
1259	Lithuania	12	140579	2843.862089	793.408555

df = pd.merge(df, cases_df[['country', 'month', 'cases_neighbors']], left_on = ['country', 'month'], right_on = ['country', 'month'], how = 'left')

countries_no_neighbors = df[df.cases_neighbors.isnull()]['country'].unique()
print(countries_no_neighbors)

['Australia' 'Jamaica' 'Japan' 'Malta' 'New Zealand' 'Philippines'
 'Singapore' 'South Korea' 'Trinidad and Tobago']

These countries don't have the metric, so take the continent average

continent_avgs = df.groupby(['continent', 'month']).new_cases_per_100k.mean().reset_index()

for c in countries_no_neighbors:
    continent = df.loc[df.country == c, 'continent'].iloc[0]
    ind = df.loc[df.country == c, 'cases_neighbors'].index
    set_values = continent_avgs.loc[continent_avgs.continent == continent, ['new_cases_per_100k']].set_index(ind)
    df.loc[df.country == c, 'cases_neighbors'] = set_values['new_cases_per_100k']

countries_no_neighbors_updated = df[df.cases_neighbors.isnull()]['country'].unique()
print(countries_no_neighbors_updated)

[]

3.3. Changing variable names, adding interaction

df.rename(columns={'idv': 'individualism_index',
                   'current_health_expenditure_of_gdp' :'health_expenditure',
                   'gdp_per_capita_constant_2010_us': 'gdp_per_capita',
                   'population_density_people_per_sq_km_of_land_area': 'population_density', 
                   }, inplace = True)

for col in ['health_expenditure', 'distance', 'gdp_per_capita']:
    df[col+'_log'] = np.log(df[col])

# Adding new changes to the model
def get_interactions(df, month_12=False):
    if month_12:
        df['individualism_gov'] = df['individualism_index'] * df['containment_health_index_avg']
        df['individualism_mob'] = df['individualism_index'] * df['mobility_index_avg']
    else:
        df['individualism_gov'] = df['individualism_index'] * df['containment_health_index']
        df['individualism_mob'] = df['individualism_index'] * df['mobility_index']
    return df

df = get_interactions(df)

df['cases_neighbors_lag'] = df['cases_neighbors'].shift(1)
df.loc[df.month == 2, 'cases_neighbors_lag'] = 0

df.to_csv("2021-01-04 final_data.csv", index=False)

df = pd.read_csv('2021-01-04 final_data.csv')

df['country'].nunique()

72

4. Results section for the paper

4.1. General table

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'continent',  'individualism_gov',
              'cases_neighbors']
df2 = df[vars_to_use]
df2.columns = ['ind', 'gdp', 'popdens', 'mob', 'containm', 'dem', 'dist', 'cont', 'ind_gov', 'neighb']

with open('summary_table.tex','w') as tf:
    tf.write(df2.describe().round(2).to_latex())

df2.columns = [f'X_{n}' for n in range(1,11)]

4.2. Individualism scores

4.2.1. Overall individualism

def get_individualism_scores(df=df, remove_last_plot=True, export_to_png=False, title=True):

    fig, axs = plt.subplots(3,4, figsize = (20,8))

    ax_list = [item for sublist in axs for item in sublist]

    for month in range(2,13):
        ax = ax_list.pop(0)
        df_ = df[df['month'] == month]
        df_ = df_[df_['new_cases_per_100k'] != 0]
        df_ = df_[df_['individualism_index'].notnull()]
        sns.regplot(x = 'new_cases_per_100k_log', y = 'individualism_index', data = df_, ax=ax)
        corr, p = pearsonr(df_['new_cases_per_100k_log'], df_['individualism_index'])
        ax.set_title(f"{calendar.month_name[month]}, $R^2$: {corr.round(2)}, p = {p.round(3)}", fontsize = 14)
        
        ax.set_ylim([0,100])

        # Set X labels
        if month in (2,6,10): ax.set_ylabel("Individualism score")
        else: ax.set_ylabel("")

        if month in (9,10,11,12): ax.set_xlabel("New cases per 100K people, log")
        else: ax.set_xlabel("")

    
    if remove_last_plot:
        fig.delaxes(axs[2,3])
    
    if title:
        fig.suptitle("Relationship between individualism and new monthly COVID-19 cases", fontsize = 24)
   
    plt.tight_layout()
    plt.subplots_adjust(top=0.9)
    
    if export_to_png:
        fig.savefig('Individualism_newcases4.png')

get_individualism_scores(export_to_png=True, title=False)

df.columns

Index(['country', 'month', 'individualism_index', 'confirmed', 'dead',
       'population', 'health_expenditure', 'gdp_per_capita',
       'population_ages_65_and_above_total', 'population_density',
       'over65_per_capita', 'population_total', 'new_cases_per_100k',
       'new_cases_total', 'new_deaths_total', 'new_cases_total_log',
       'new_cases_per_100k_log', 'new_deaths_total_log', 'mobility_index',
       'containment_health_index', 'democracy_index', 'capital', 'distance',
       'continent', 'confirmed_log', 'cases_neighbors', 'distance_log',
       'individualism_gov', 'individualism_mob', 'health_expenditure_log',
       'gdp_per_capita_log', 'gdp'],
      dtype='object')

month = 12
def label_point(x, y, val, ax):
    a = pd.concat({'x': x, 'y': y, 'val': val}, axis=1)
    for i, point in a.iterrows():
        if point['val'] in ['Australia', 'New Zealand', 'Vietnam']:
            ax.text(point['x']+.25, point['y'], str(point['val']))


fig, ax = plt.subplots(1,1,figsize=(8,7))
df_ = df[df['month'] == month]
df_ = df_[df_['new_cases_per_100k'] != 0]
df_ = df_[df_['individualism_index'].notnull()]
df_2 = df_[~df_.country.isin(['Australia', 'New Zealand', 'Vietnam'])]

f1 = sns.regplot(x = 'new_cases_per_100k_log', y = 'individualism_index', data = df_, ax=ax)
f2 = sns.regplot(x = 'new_cases_per_100k_log', y = 'individualism_index', data = df_2, ax=ax, 
           scatter_kws = {'color': 'midnightblue'}, line_kws = {'color': 'midnightblue'})
corr, p = pearsonr(df_['new_cases_per_100k_log'], df_['individualism_index'])
print(corr,p)
corr2, p2 = pearsonr(df_2['new_cases_per_100k_log'], df_2['individualism_index'])
print(corr2,p2)


#ax.set_title(f"{calendar.month_name[month]}, $R^2$: {corr.round(2)}, p = {p.round(3)}")

blue_patch = mpatches.Patch(color='tab:blue', label='Line of best fit, all data')
midnight_patch = mpatches.Patch(color='midnightblue', label='Line of best fit, selected data')

#plt.legend(handles=[red_patch, midnight_patch], bbox_to_anchor = (1.01, 1), loc = 'upper left', frameon=True)
plt.legend(handles=[blue_patch, midnight_patch], loc = 'lower right', frameon=False)

label_point(df_.new_cases_per_100k_log, df_.individualism_index, df_.country, plt.gca())

fig.savefig('month_12.png')

0.31727538808414757 0.0070178711833126855
0.5207701239060172 5.298551251561445e-06

4.2.2. Cumulative individualism

df['confirmed_per_100k'] = (df['confirmed'] / df['population']) * 100_000
df['confirmed_per_100k_log'] = np.log(df['confirmed_per_100k'] + 0.0000000000001)

def get_individualism_scores(df=df, remove_last_plot=True, export_to_png=False, title=True, cumulative=False):
    if cumulative: individualism='confirmed_per_100k_log'
    else: individualism = 'new_cases_per_100k_log'

    fig, axs = plt.subplots(3,4, figsize = (20,8))

    ax_list = [item for sublist in axs for item in sublist]

    for month in range(2,13):
        ax = ax_list.pop(0)
        df_ = df[df['month'] == month]
        
        df_ = df_[df_['new_cases_per_100k'] != 0]
        df_ = df_[df_['individualism_index'].notnull()]
        sns.regplot(x = individualism, y = 'individualism_index', data = df_, ax=ax)
        corr, p = pearsonr(df_[individualism], df_['individualism_index'])
        ax.set_title(f"{calendar.month_name[month]}, $R^2$: {corr.round(2)}, p = {p.round(3)}")
        
        ax.set_ylim([0,100])

        # Set X labels
        if month in (2,6,10): ax.set_ylabel("Individualism score")
        else: ax.set_ylabel("")
        
        if not cumulative:
            if month in (10,11,12): ax.set_xlabel("New cases per 100K people, log")
            else: ax.set_xlabel("")
        else:
            if month in (9,10,11,12): ax.set_xlabel("Cumulative cases per 100K people, log")
            else: ax.set_xlabel("")
    
    if remove_last_plot:
        fig.delaxes(axs[2,3])
    
    if not cumulative:
        if title:
            fig.suptitle("Relationship between individualism and new monthly COVID-19 cases", fontsize = 16)
   
    plt.tight_layout()
    plt.subplots_adjust(top=0.9)
    
    if not cumulative:
        if export_to_png:
            fig.savefig('Individualism_newcases3.png')
    else:     
        if export_to_png:
            fig.savefig('Individualism_cumulativecases3.png')

get_individualism_scores(title=False, cumulative=True, export_to_png=True)

get_individualism_scores(title=False, cumulative=False, export_to_png=True)

4.2.3. Relationship between all variables

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'continent',  'individualism_gov',
              'cases_neighbors']

#sns.regplot(x=vars_to_use, y='individualism_index', data=df_newest)

sns.pairplot(df_newest[vars_to_use], y_vars='individualism_index')

<seaborn.axisgrid.PairGrid at 0x1efd73afdc0>

sns.pairplot(df[vars_to_use], hue = 'continent')

<seaborn.axisgrid.PairGrid at 0x1efc2fd58e0>

4.2.4. Relationship between government intervention and invidualism

# Establish connection

conn = psycopg2.connect(
    host='covid19db.org',
    port=5432,
    dbname='covid19',
    user='covid19',
    password='covid19')
cur = conn.cursor()

def get_gov_data(threshold=0.8):
    """Extract governmental data from the postgres database and checks for high similarities between entries
    
    Args:
        threshold (float): the threshold for deciding whether strings are similar
        
    Returns:
        gov_df (dataframe): dataframe containing government response information
    """

    # Extract the data
    sql_command = """
    SELECT date, country,c6_Stay_at_home_requirements,  c6_Flag
    FROM government_response
    WHERE source = 'GOVTRACK'
    """
    gov_df = pd.read_sql(sql_command, conn)
    gov_df['date'] = pd.to_datetime(gov_df['date'])
    
    # Inspect countries for similarities (to try to find duplicate entries)
    countries_lower = [c.lower() for c in gov_df['country'].unique()]
    
    print("Countries with similar strings: ")
    for c1, c2 in itertools.combinations(countries_lower, 2):
        if SequenceMatcher(None, c1, c2).ratio() > threshold:
            print(f"Country 1: {c1} Country 2: {c2}")
            
    return gov_df


def get_stay_at_home_metrics(gov_df):
    """Add additional stay-at-home metrics to the dataframe

    The function finds the first time a government imposed stay at home requirements
    on a national scale that are at least 2 or 3 in strength, as measured by the
    C6 index on the OXCOVID-19 database. Local restrictions are not taken into account.
    
    The function calculates:
    - the number of days before and after the introduced requirements for each day and country
    - the number of weeks before and after the introduced requirements for each day and country
    
    The weeks are calculated on a daily basis as opposed to taking calendar weeks. For example,
    the first 7 days after the introduction of the requirements are considered week 1, regardless
    of the day of the week. Note that this calculation does not take into account if a government
    uplifted its requirements.
    
    Args:
        gov_df (dataframe): Dataframe containing government response information
        
    Returns:
        gov_df (dataframe): New dataframe that includes additional columns on government response
    """
    
    # Get countries with stay at home requirements on a national level
    countries_with_req = gov_df.loc[(gov_df['c6_stay_at_home_requirements'].isin([2,3])), 'country'].unique()
    gov_df = gov_df[gov_df['country'].isin(countries_with_req)].copy()
    gov_df.sort_values(['country', 'date'], inplace = True)
    gov_df.index = pd.RangeIndex(len(gov_df))
    
    # Loop over all the countries
    for country in countries_with_req:
        
        # Filter country specific values
        gov_filter = gov_df.country == country        
        first_country_filter = gov_df.loc[gov_filter].index.min()
        
        # Get the id of stay at home requirements
        home_id_any_level = gov_df.loc[gov_filter, 'c6_stay_at_home_requirements'].isin([2,3]).idxmax()
        #c5_flag = (gov_df.loc[gov_filter, 'c6_flag'] == 1).idxmax()
        home_id = home_id_any_level

        # Get days before and after filters
        days_before_filter = gov_df.index < home_id
        days_after_filter = gov_df.index >= home_id

        # Assign the number of days before and after for each country
        gov_df.loc[gov_filter & days_before_filter, 'days_after'] = range(first_country_filter-home_id, 0, 1)
        gov_df.loc[gov_filter & days_after_filter, 'days_after'] = range(0, np.sum(gov_filter & days_after_filter))
        gov_df.loc[gov_filter, 'weeks_after'] = gov_df.loc[gov_filter, 'days_after'].map(
            lambda day: math.ceil(day/7) if day > 0 else math.floor(day/7))
        
  
    return gov_df


gov_df = get_gov_data()

# Excluding "Viet nam" since it is entered two times
gov_df = gov_df[gov_df['country'] != 'Viet Nam']

# Extracting additional metrics for plotting
gov_df = get_stay_at_home_metrics(gov_df)

Countries with similar strings: 
Country 1: iceland Country 2: ireland
Country 1: australia Country 2: austria
Country 1: vietnam Country 2: viet nam
Country 1: niger Country 2: nigeria
Country 1: gambia Country 2: zambia

gov_df[gov_df.country == 'United States'].sort_values('date')

	date	country	c6_stay_at_home_requirements	c6_flag	days_after	weeks_after

gov_df[gov_df.country == 'United States']['c6_stay_at_home_requirements'].max()

nan

df2 = pd.read_excel("6-dimensions-for-website-2015-08-16.xls")

df2 = df2[['country', 'idv']]

df2.head()

	country	idv
0	Africa East	27.0
1	Africa West	20.0
2	Albania	20.0
3	Algeria	35.0
4	Andorra	NaN

gov_df = gov_df.merge(df2[['country', 'idv']], left_on='country', right_on='country', how='left')

gov_df[gov_df.idv.notnull()].country.nunique()

67

gov_df = gov_df[gov_df.idv.notnull()]

cases_df = get_cases(conn)
cases_df = calculate_capita_metrics(cases_df)
cases_df = get_daily_growth(cases_df) 
cases_df = daily_growth_check(cases_df, drop_countries = True)

A total of 30 entries are excluded from the initial dataset since they do not have data for Population.
These are: Mayotte, Other continent, Saint Helena, Oceania, Pitcairn Islands, Martinique, Reunion, Wallis and Futuna, Guernsey, Montserrat, Cook Islands, Kosovo, Asia, French Guiana, Bonaire, Sint Eustatius and Saba, Tokelau, Saint-Barthélemy, America, Saint Pierre and Miquelon, Falkland Islands, Taiwan, Niue, Anguilla, World, Guadeloupe, Africa, Vatican City, Western Sahara, Europe, Jersey

There are 64 cases of negative daily growth in cases from the data

Dropped 4 countries from further analysis: Benin, Ecuador, Puerto Rico, São Tomé and Príncipe.

gov_df = gov_df.merge(cases_df[['date', 'country', 'new_cases_per_100K']], on = ['date', 'country'], how = 'left')

def get_categories(v):
    """Divide a number into distinct categories of 10. For instance, '5' becomes '0-10' and 23 becomes '20-30'
    
    Args: 
        v (float): a number
    
    Returns:
        range_value (string): a range between the two numbers
        
    """
    
    v1 = str(int(v/25)*25)
    v2 = str(int(v1) + 25)
    range_value = v1 + '-' + v2
    return range_value


def get_agg_rural_data(gov_df):
    """Get aggregated data based on the dataframe and prepares it for the right
    format for plotting
    
    Args:
        gov_df (dataframe): Dataframe containing government response information
 
    Returns:
        df_at_home_agg (dataframe): Aggregated information of the previous dataframe
    """
    
    # Create rural categories
    gov_df['idv_categ'] = gov_df['idv'].map(get_categories)
    
    # Create the values to be plotted
    df_at_home_agg = pd.pivot_table(gov_df[gov_df['weeks_after'].between(-8, 15)],
               index = ['idv_categ'],
               columns = 'weeks_after',
              values = 'new_cases_per_100K',
              aggfunc = 'mean').drop(0, axis = 1)
    
    # Convert weeks to intigers
    df_at_home_agg.columns = [int(x) for x in df_at_home_agg.columns]
    
    # Reverse order to ensure it is from low to high
    df_at_home_agg = df_at_home_agg.loc[df_at_home_agg.index[::-1]]
    
    return df_at_home_agg

df_at_home_agg = get_agg_rural_data(gov_df)

df_at_home_agg_log = np.log(df_at_home_agg)

def plot_cases(df_at_home_agg, set_params_max=True, vmin=0, vmax = 6):
    """Plot a heatmap of number of new weekly cases per 100K by rural category and week after
    the introduction of the nation-wide stay at home requirements.
    
    Args:
        df_at_home_agg (dataframe): Aggregated information on information to plot
        
    Returns:
        None
    """

    # Set palette
    cmap = sns.dark_palette("#69d", reverse = True, as_cmap=True)

    # Create subplot
    fig, ax = plt.subplots(1,1, figsize = (15,5))
    fig.suptitle('Figure 8. Number of new weekly cases per 100K people after stay-at-home requirement introduction', fontsize=15)

    # Create heatmap and params
    if set_params_max:
        sns.heatmap(df_at_home_agg, vmin = vmin, vmax = vmax, cmap = cmap, linecolor = 'white', linewidth = 0.01, ax = ax)
    else:
        sns.heatmap(df_at_home_agg, cmap = cmap, linecolor = 'white', linewidth = 0.01, ax = ax)
    ax.vlines([8], *ax.get_xlim(), linestyle = 'solid', colors = 'black', label = 'test', lw = 3)
    plt.text(6,0,'Requirements introduced\n', fontdict = {'weight': 100, 'size': 12})
    ax.set_xlabel('Weeks after the introduction of nation-wide stay-at-home requirements')
    ax.set_ylabel('Rural population in the country, %')
    plt.yticks(rotation=0);
    

df.columns

Index(['country', 'month', 'individualism_index', 'confirmed', 'dead',
       'population', 'health_expenditure', 'gdp_per_capita',
       'population_ages_65_and_above_total', 'population_density',
       'over65_per_capita', 'population_total', 'new_cases_per_100k',
       'new_cases_total', 'new_deaths_total', 'new_cases_total_log',
       'new_cases_per_100k_log', 'new_deaths_total_log', 'mobility_index',
       'containment_health_index', 'democracy_index', 'capital', 'distance',
       'continent', 'confirmed_log', 'cases_neighbors', 'distance_log',
       'individualism_gov', 'individualism_mob', 'health_expenditure_log',
       'gdp_per_capita_log'],
      dtype='object')

index = df.groupby('country').agg({'containment_health_index': ['min', 'mean', 'max', 'std']})

index['containment_health_index']['min

38.30793103448276

plot_cases(df_at_home_agg)

plot_cases(df_at_home_agg_log, set_params_max=True, vmin= -8, vmax = 2.4)

def gov_intervention_plot(gov_df):
    """Plot the dates of when the government intervened for the first time in different rural regions.
    
    Args:
        gov_df (dataframe): Dataframe containing government response information
        
    Returns:
        None
    """
    
    # Get days when the government intervened with the policy
    df_plot = gov_df.loc[gov_df['days_after'] == 0, ['date', 'rural_category']]
    
    # Get date format
    date_format = mdates.DateFormatter('%b')
    
    # Create the plot
    fig, axs = plt.subplots(1,3, figsize=(15,4), sharex = True)
    fig.suptitle('Figure 7. Covid-19 and the first time of national stay at home requirements by rural area type')

    # Dictionary for looping
    rural_dict = {'Low': 0,
     'Medium': 1,
     'High': 2}

    # Configure each graph in a loop
    for category, i in rural_dict.items():
        sns.histplot(df_plot[df_plot['rural_category'] == category], x = 'date', ax = axs[i], bins = 10)
        axs[i].set_title(f"Rural category: {category}")
        axs[i].xaxis.set_major_formatter(date_format)
        axs[i].set_ylabel("Number of countries")
        if i != 0: axs[i].set_ylabel("")
   
    
    # Add annotation
    annotation_text = """Note: The y-axes are different for each plot to showcase the relative distributions within each group"""
    annotate_plot(annotation_text, top = 0.8, bottom = 0.2,  x1=.06, x2=.05)

5. Running regressions

df = pd.read_csv('2021-01-04 final_data.csv')

df.head()

	country	month	individualism_index	confirmed	dead	population	health_expenditure	gdp_per_capita	population_ages_65_and_above_total	population_density	...	capital	distance	continent	confirmed_log	cases_neighbors	distance_log	individualism_gov	individualism_mob	health_expenditure_log	gdp_per_capita_log
0	Argentina	2.0	46.0	0.0	0.0	44938712.0	9.124315	9729.141574	5052508.0	16.25851	...	Buenos Aires	19206.559549	SA	-29.933606	0.000474	9.863007	353.740000	-32.791687	2.210943	9.182881
1	Argentina	3.0	46.0	820.0	20.0	44938712.0	9.124315	9729.141574	5052508.0	16.25851	...	Buenos Aires	19206.559549	SA	6.709304	5.122697	9.863007	2072.641290	-1506.103166	2.210943	9.182881
2	Argentina	4.0	46.0	4201.0	207.0	44938712.0	9.124315	9729.141574	5052508.0	16.25851	...	Buenos Aires	19206.559549	SA	8.343078	23.515800	9.863007	3757.740000	-3130.225314	2.210943	9.182881
3	Argentina	5.0	46.0	14702.0	510.0	44938712.0	9.124315	9729.141574	5052508.0	16.25851	...	Buenos Aires	19206.559549	SA	9.595739	138.163769	9.863007	3611.756774	-2817.033416	2.210943	9.182881
4	Argentina	6.0	46.0	59933.0	1245.0	44938712.0	9.124315	9729.141574	5052508.0	16.25851	...	Buenos Aires	19206.559549	SA	11.000983	318.002633	9.863007	3575.672000	-2429.974159	2.210943	9.182881

5 rows × 31 columns

def export_csv(df, export_no_two=True, 
               export_dummies=True, 
               export_dummies_no_two=False,
               mean_vars_export=False,
               vars_to_mean = ['individualism_index',
                             'health_expenditure',
                             'gdp_per_capita',
                             'over65_per_capita',
                             'population_density',
                             'mobility_index',
                             'containment_health_index',
                             'democracy_index',
                             'distance']):
    
    if export_no_two:
        df[df.month != 2].to_csv('2021-01-04 clean_data_from_3.csv', index=False)
        
    if export_dummies:
        df_cont = pd.concat((df.drop('continent', axis=1), pd.get_dummies(df['continent'], prefix = 'continent').iloc[:,0:5]), axis=1)
        df_cont.to_csv("2021-01-03 clean_data_w_dummies.csv", index=False)
        
    if export_dummies_no_two:
        df_cont[df_cont.month != 2].to_csv("2021-01-03 clean_data_w_dummies.csv", index=False)
        
    if mean_vars_export:
       
        vars_no_mean = [x for x in df_cont.columns if x not in vars_to_mean]
        df_cont_mean_centered = pd.concat((df_cont[vars_no_mean], df_cont[vars_to_mean] - df_cont[vars_to_mean].mean()), axis = 1)
        df_cont_mean_centered[df_cont_mean_centered.month != 2].to_csv('2021-01-03 clean_data_w_dummies_centered.csv')

5.1. Regression with total cases as of date

5.1.1. Getting interaction effects

df_newest = df[df.month==12]

df_newest = df_newest.set_index('country')

df_newest['mobility_index_avg'] = df.groupby('country').mobility_index.mean()
df_newest['containment_health_index_avg'] = df.groupby('country').containment_health_index.mean()

# Adding new changes to the model
def get_interactions(df, month_12=False):
    if month_12:
        df['individualism_gov'] = df['individualism_index'] * df['containment_health_index_avg']
        df['individualism_mob'] = df['individualism_index'] * df['mobility_index_avg']
    else:
        df['individualism_gov'] = df['individualism_index'] * df['containment_health_index']
        df['individualism_mob'] = df['individualism_index'] * df['mobility_index']
    return df

df_newest = get_interactions(df_newest, month_12=True)

df_newest.columns

Index(['month', 'individualism_index', 'confirmed', 'dead', 'population',
       'health_expenditure', 'gdp_per_capita',
       'population_ages_65_and_above_total', 'population_density',
       'over65_per_capita', 'population_total', 'new_cases_per_100k',
       'new_cases_total', 'new_deaths_total', 'new_cases_total_log',
       'new_cases_per_100k_log', 'new_deaths_total_log', 'mobility_index',
       'containment_health_index', 'democracy_index', 'capital', 'distance',
       'continent', 'confirmed_log', 'cases_neighbors', 'distance_log',
       'individualism_gov', 'individualism_mob', 'health_expenditure_log',
       'gdp_per_capita_log', 'season', 'mobility_index_avg',
       'containment_health_index_avg'],
      dtype='object')

5.1.2. Results with Tanzania

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'continent',  'individualism_gov',
              'cases_neighbors']

fig, ax, = plt.subplots(figsize=(12,7))
sns.heatmap(df_newest[vars_to_use].corr(), annot=True)

<AxesSubplot:>

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index_avg', 'containment_health_index_avg', 'democracy_index', 'distance_log', 'continent', 'individualism_gov', 'cases_neighbors']
results_total2 = smf.ols('confirmed_log ~ ' + ' + '.join(vars_to_use), data = df_newest[df_newest != 'Tanzania']).fit()

results_total = smf.ols('confirmed_log ~ ' + ' + '.join(vars_to_use), data = df_newest).fit()

results_total.summary()

OLS Regression Results

Dep. Variable:	confirmed_log	R-squared:	0.519
Model:	OLS	Adj. R-squared:	0.401
Method:	Least Squares	F-statistic:	4.390
Date:	Thu, 07 Jan 2021	Prob (F-statistic):	3.11e-05
Time:	08:16:26	Log-Likelihood:	-126.84
No. Observations:	72	AIC:	283.7
Df Residuals:	57	BIC:	317.8
Df Model:	14
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Intercept	-0.6880	7.282	-0.094	0.925	-15.269	13.893
continent[T.AS]	2.2030	1.114	1.977	0.053	-0.028	4.434
continent[T.EU]	1.5799	1.001	1.578	0.120	-0.424	3.584
continent[T.N.A.]	0.6526	0.992	0.658	0.513	-1.334	2.639
continent[T.OC]	-2.3992	1.457	-1.647	0.105	-5.317	0.519
continent[T.SA]	1.9441	1.122	1.732	0.089	-0.303	4.191
individualism_index	-0.0312	0.067	-0.464	0.645	-0.166	0.104
gdp_per_capita	-7.994e-06	1.3e-05	-0.615	0.541	-3.4e-05	1.8e-05
population_density	-0.0001	0.000	-0.657	0.514	-0.001	0.000
mobility_index_avg	0.0098	0.024	0.406	0.686	-0.039	0.058
containment_health_index_avg	0.0597	0.055	1.084	0.283	-0.051	0.170
democracy_index	-0.0118	0.017	-0.713	0.479	-0.045	0.021
distance_log	0.8928	0.719	1.242	0.219	-0.547	2.333
individualism_gov	0.0013	0.001	1.039	0.303	-0.001	0.004
cases_neighbors	0.0002	0.001	0.420	0.676	-0.001	0.001

Omnibus:	7.626	Durbin-Watson:	1.731
Prob(Omnibus):	0.022	Jarque-Bera (JB):	7.171
Skew:	-0.620	Prob(JB):	0.0277
Kurtosis:	3.922	Cond. No.	1.34e+06

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.34e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

results_df = pd.DataFrame()
results_df = results_df.append(results.pvalues, ignore_index=True)
params_ = results.params
p_ = results.pvalues

5.1.3. Results without Tanzania

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index_avg', 'containment_health_index_avg', 'democracy_index', 'distance_log', 'continent', 'individualism_gov', 'cases_neighbors']

df_newest2 = df_newest[df_newest.index != 'Tanzania']

results_total2 = smf.ols('confirmed_log ~ ' + ' + '.join(vars_to_use), data = df_newest[df_newest.index != 'Tanzania']).fit()
results_total2.summary()

OLS Regression Results

Dep. Variable:	confirmed_log	R-squared:	0.470
Model:	OLS	Adj. R-squared:	0.338
Method:	Least Squares	F-statistic:	3.553
Date:	Thu, 07 Jan 2021	Prob (F-statistic):	0.000348
Time:	14:42:34	Log-Likelihood:	-124.36
No. Observations:	71	AIC:	278.7
Df Residuals:	56	BIC:	312.7
Df Model:	14
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Intercept	1.8644	7.447	0.250	0.803	-13.053	16.782
continent[T.AS]	2.0664	1.109	1.863	0.068	-0.155	4.288
continent[T.EU]	1.4363	0.998	1.439	0.156	-0.563	3.435
continent[T.N.A.]	0.5697	0.985	0.578	0.565	-1.404	2.544
continent[T.OC]	-2.6646	1.457	-1.829	0.073	-5.584	0.255
continent[T.SA]	1.8619	1.114	1.671	0.100	-0.370	4.094
individualism_index	-0.0606	0.070	-0.866	0.390	-0.201	0.080
gdp_per_capita	-8.437e-06	1.29e-05	-0.654	0.516	-3.43e-05	1.74e-05
population_density	-0.0001	0.000	-0.665	0.509	-0.001	0.000
mobility_index_avg	0.0047	0.024	0.196	0.846	-0.044	0.053
containment_health_index_avg	0.0180	0.062	0.290	0.773	-0.107	0.143
democracy_index	-0.0109	0.016	-0.662	0.511	-0.044	0.022
distance_log	0.8620	0.713	1.208	0.232	-0.567	2.291
individualism_gov	0.0018	0.001	1.437	0.156	-0.001	0.004
cases_neighbors	0.0002	0.001	0.264	0.793	-0.001	0.001

Omnibus:	9.036	Durbin-Watson:	1.726
Prob(Omnibus):	0.011	Jarque-Bera (JB):	8.788
Skew:	-0.715	Prob(JB):	0.0124
Kurtosis:	3.962	Cond. No.	1.38e+06

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.38e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

result_summ = summary_col([results_total2], stars=True)
res_df = result_summ.tables[0]
res_df.columns = ['Cumulative']

with open('cumulative_regression.tex','w') as tf:
    tf.write(res_df.to_latex())

5.2. Regression for different months

df.columns

Index(['country', 'month', 'individualism_index', 'confirmed', 'dead',
       'population', 'health_expenditure', 'gdp_per_capita',
       'population_ages_65_and_above_total', 'population_density',
       'over65_per_capita', 'population_total', 'new_cases_per_100k',
       'new_cases_total', 'new_deaths_total', 'new_cases_total_log',
       'new_cases_per_100k_log', 'new_deaths_total_log', 'mobility_index',
       'containment_health_index', 'democracy_index', 'capital', 'distance',
       'continent', 'confirmed_log', 'cases_neighbors', 'distance_log',
       'individualism_gov', 'individualism_mob', 'health_expenditure_log',
       'gdp_per_capita_log'],
      dtype='object')

df['containment_health_index'].max()

87.693

'new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use)

'new_cases_per_100k_log ~ individualism_index + gdp_per_capita + population_density + mobility_index + containment_health_index + democracy_index + distance_log + continent + individualism_gov + cases_neighbors'

result_dict = {}

df3 = df[df.country != 'Tanzania'].copy()

# Create many variables in a for-loop

monthly_vars = {}
vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'continent',  'individualism_gov',
              'cases_neighbors']

for i in range(2,13):
    results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df[df.month == i]).fit()
    monthly_vars['month_{}'.format(i)] = results

for k,v in monthly_vars.items():
    monthly_vars[k] = v.get_robustcov_results()

rs_list = list(monthly_vars.values())

result_summ = summary_col(rs_list[0:6], stars=True)
res_df1 = result_summ.tables[0]
res_df1.columns = [f'Month_{x}' for x in range(2,8)]

with open('summary_monthly1.tex','w') as tf:
    tf.write(res_df1.to_latex())

result_summ = summary_col(rs_list[6:], stars=True)
res_df2 = result_summ.tables[0]
res_df2.columns = [f'Month_{x}' for x in range(8,13)]
with open('summary_monthly2.tex','w') as tf:
    tf.write(res_df2.to_latex())

res_df1 = results_months1.tables[0]
res_df1.columns = [f'Month_{x}' for x in range(2,8)]

res_df2 = results_months2.tables[0]
res_df2.columns = [f'Month_{x}' for x in range(8,13)]

with open('summary_seasonal.tex','w') as tf:
    tf.write(res_df.to_latex())

df3 = df[df.country != 'Tanzania'].copy()

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'continent',  'individualism_gov',
              'cases_neighbors']

for month in range(2,13):
    results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df[df.month == month]).fit()
    print(f"\n\n------------------- MONTH: {month} -----------------------")
    print(results.summary())
    result_dict[str(month) + '_pvalues'] = results.pvalues
    result_dict[str(month) + '_params'] = results.params

------------------- MONTH: 2 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.442
Model:                                OLS   Adj. R-squared:                  0.305
Method:                     Least Squares   F-statistic:                     3.222
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           0.000883
Time:                            15:04:27   Log-Likelihood:                -202.82
No. Observations:                      72   AIC:                             435.6
Df Residuals:                          57   BIC:                             469.8
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                   37.8081     23.409      1.615      0.112      -9.067      84.683
continent[T.AS]             -2.7975      3.214     -0.870      0.388      -9.233       3.638
continent[T.EU]             -0.9357      2.371     -0.395      0.695      -5.684       3.813
continent[T.N.A.]            0.5199      2.528      0.206      0.838      -4.543       5.583
continent[T.OC]             -0.5764      4.376     -0.132      0.896      -9.338       8.186
continent[T.SA]              1.2658      3.044      0.416      0.679      -4.831       7.362
individualism_index          0.0022      0.052      0.042      0.967      -0.102       0.107
gdp_per_capita            6.134e-05   3.89e-05      1.577      0.120   -1.65e-05       0.000
population_density           0.0004      0.001      0.609      0.545      -0.001       0.002
mobility_index               0.0700      0.150      0.466      0.643      -0.231       0.371
containment_health_index    -0.0772      0.160     -0.482      0.632      -0.398       0.244
democracy_index              0.0116      0.050      0.232      0.818      -0.089       0.112
distance_log                -5.4697      2.426     -2.254      0.028     -10.328      -0.611
individualism_gov            0.0043      0.003      1.335      0.187      -0.002       0.011
cases_neighbors              0.4718      2.088      0.226      0.822      -3.709       4.653
==============================================================================
Omnibus:                        2.587   Durbin-Watson:                   2.640
Prob(Omnibus):                  0.274   Jarque-Bera (JB):                1.577
Skew:                          -0.042   Prob(JB):                        0.454
Kurtosis:                       2.280   Cond. No.                     1.50e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.5e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- MONTH: 3 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.788
Model:                                OLS   Adj. R-squared:                  0.737
Method:                     Least Squares   F-statistic:                     15.18
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           2.22e-14
Time:                            15:04:27   Log-Likelihood:                -101.45
No. Observations:                      72   AIC:                             232.9
Df Residuals:                          57   BIC:                             267.0
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -12.5020      5.346     -2.339      0.023     -23.207      -1.797
continent[T.AS]              1.8000      0.800      2.249      0.028       0.197       3.403
continent[T.EU]              2.2048      0.554      3.983      0.000       1.096       3.313
continent[T.N.A.]            0.7048      0.613      1.149      0.255      -0.524       1.933
continent[T.OC]              1.1584      1.002      1.156      0.253      -0.848       3.165
continent[T.SA]              0.3635      0.743      0.489      0.627      -1.125       1.852
individualism_index          0.0403      0.030      1.360      0.179      -0.019       0.100
gdp_per_capita            3.353e-05   9.21e-06      3.642      0.001    1.51e-05     5.2e-05
population_density        6.206e-05      0.000      0.397      0.693      -0.000       0.000
mobility_index              -0.0509      0.022     -2.326      0.024      -0.095      -0.007
containment_health_index     0.0256      0.032      0.788      0.434      -0.039       0.090
democracy_index              0.0153      0.012      1.283      0.205      -0.009       0.039
distance_log                 0.9424      0.545      1.731      0.089      -0.148       2.033
individualism_gov           -0.0009      0.001     -1.198      0.236      -0.002       0.001
cases_neighbors              0.0040      0.004      1.017      0.313      -0.004       0.012
==============================================================================
Omnibus:                        4.141   Durbin-Watson:                   1.971
Prob(Omnibus):                  0.126   Jarque-Bera (JB):                3.360
Skew:                          -0.395   Prob(JB):                        0.186
Kurtosis:                       3.705   Cond. No.                     1.40e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.4e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- MONTH: 4 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.735
Model:                                OLS   Adj. R-squared:                  0.669
Method:                     Least Squares   F-statistic:                     11.26
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           9.64e-12
Time:                            15:04:27   Log-Likelihood:                -97.324
No. Observations:                      72   AIC:                             224.6
Df Residuals:                          57   BIC:                             258.8
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -10.1185      5.156     -1.963      0.055     -20.443       0.206
continent[T.AS]              2.0577      0.736      2.794      0.007       0.583       3.532
continent[T.EU]              2.6559      0.511      5.196      0.000       1.632       3.679
continent[T.N.A.]            1.2652      0.576      2.197      0.032       0.112       2.419
continent[T.OC]             -0.2664      1.020     -0.261      0.795      -2.309       1.777
continent[T.SA]              1.4494      0.686      2.113      0.039       0.076       2.823
individualism_index          0.0192      0.048      0.402      0.689      -0.076       0.115
gdp_per_capita            2.599e-05   9.34e-06      2.782      0.007    7.28e-06    4.47e-05
population_density           0.0003      0.000      2.134      0.037    1.96e-05       0.001
mobility_index              -0.0270      0.012     -2.244      0.029      -0.051      -0.003
containment_health_index    -0.0269      0.028     -0.963      0.340      -0.083       0.029
democracy_index             -0.0104      0.011     -0.955      0.344      -0.032       0.011
distance_log                 1.2390      0.508      2.437      0.018       0.221       2.257
individualism_gov        -4.832e-05      0.001     -0.069      0.945      -0.001       0.001
cases_neighbors              0.0007      0.003      0.286      0.776      -0.004       0.006
==============================================================================
Omnibus:                        2.141   Durbin-Watson:                   1.472
Prob(Omnibus):                  0.343   Jarque-Bera (JB):                2.068
Skew:                          -0.399   Prob(JB):                        0.356
Kurtosis:                       2.772   Cond. No.                     1.43e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.43e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- MONTH: 5 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.272
Model:                                OLS   Adj. R-squared:                  0.093
Method:                     Least Squares   F-statistic:                     1.518
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):              0.134
Time:                            15:04:27   Log-Likelihood:                -161.90
No. Observations:                      72   AIC:                             353.8
Df Residuals:                          57   BIC:                             388.0
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                   -3.6385     12.290     -0.296      0.768     -28.250      20.973
continent[T.AS]              0.7656      1.818      0.421      0.675      -2.874       4.406
continent[T.EU]              1.8166      1.258      1.444      0.154      -0.702       4.336
continent[T.N.A.]            0.3459      1.479      0.234      0.816      -2.615       3.307
continent[T.OC]             -2.3787      2.417     -0.984      0.329      -7.218       2.460
continent[T.SA]              2.5601      1.901      1.347      0.183      -1.247       6.367
individualism_index          0.0229      0.119      0.193      0.847      -0.214       0.260
gdp_per_capita            1.192e-05   2.22e-05      0.538      0.593   -3.25e-05    5.63e-05
population_density           0.0004      0.000      1.039      0.303      -0.000       0.001
mobility_index              -0.0229      0.026     -0.881      0.382      -0.075       0.029
containment_health_index     0.0011      0.073      0.015      0.988      -0.145       0.147
democracy_index             -0.0374      0.028     -1.348      0.183      -0.093       0.018
distance_log                 0.5286      1.214      0.435      0.665      -1.902       2.959
individualism_gov            0.0002      0.002      0.141      0.888      -0.003       0.004
cases_neighbors              0.0028      0.006      0.442      0.660      -0.010       0.015
==============================================================================
Omnibus:                       98.090   Durbin-Watson:                   1.730
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2042.647
Skew:                          -4.075   Prob(JB):                         0.00
Kurtosis:                      27.788   Cond. No.                     1.39e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.39e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- MONTH: 6 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.447
Model:                                OLS   Adj. R-squared:                  0.311
Method:                     Least Squares   F-statistic:                     3.290
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           0.000723
Time:                            15:04:27   Log-Likelihood:                -154.18
No. Observations:                      72   AIC:                             338.4
Df Residuals:                          57   BIC:                             372.5
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -22.8302     10.834     -2.107      0.040     -44.525      -1.135
continent[T.AS]              3.1305      1.642      1.906      0.062      -0.159       6.419
continent[T.EU]              3.5579      1.143      3.113      0.003       1.269       5.847
continent[T.N.A.]            1.7705      1.364      1.298      0.199      -0.961       4.502
continent[T.OC]              1.2898      2.408      0.536      0.594      -3.533       6.113
continent[T.SA]              2.2152      2.021      1.096      0.278      -1.831       6.262
individualism_index          0.0396      0.087      0.454      0.652      -0.135       0.214
gdp_per_capita            1.392e-05   1.95e-05      0.715      0.477    -2.5e-05    5.29e-05
population_density           0.0002      0.000      0.710      0.481      -0.000       0.001
mobility_index               0.0026      0.023      0.115      0.908      -0.043       0.048
containment_health_index     0.1374      0.058      2.358      0.022       0.021       0.254
democracy_index             -0.0193      0.025     -0.776      0.441      -0.069       0.030
distance_log                 1.7589      1.080      1.629      0.109      -0.404       3.922
individualism_gov           -0.0007      0.001     -0.501      0.619      -0.003       0.002
cases_neighbors              0.0004      0.005      0.090      0.928      -0.009       0.010
==============================================================================
Omnibus:                       45.252   Durbin-Watson:                   1.657
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              232.495
Skew:                          -1.711   Prob(JB):                     3.27e-51
Kurtosis:                      11.111   Cond. No.                     1.37e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.37e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- MONTH: 7 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.488
Model:                                OLS   Adj. R-squared:                  0.363
Method:                     Least Squares   F-statistic:                     3.885
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           0.000128
Time:                            15:04:27   Log-Likelihood:                -151.81
No. Observations:                      72   AIC:                             333.6
Df Residuals:                          57   BIC:                             367.8
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -19.9097      9.686     -2.055      0.044     -39.307      -0.513
continent[T.AS]              2.5675      1.525      1.683      0.098      -0.487       5.622
continent[T.EU]              3.8146      1.151      3.315      0.002       1.510       6.119
continent[T.N.A.]            1.1589      1.426      0.813      0.420      -1.696       4.014
continent[T.OC]              1.0554      2.078      0.508      0.613      -3.105       5.216
continent[T.SA]              0.8507      1.877      0.453      0.652      -2.909       4.610
individualism_index          0.0127      0.066      0.193      0.847      -0.119       0.145
gdp_per_capita            2.398e-05   1.87e-05      1.281      0.205   -1.35e-05    6.15e-05
population_density           0.0002      0.000      0.551      0.584      -0.000       0.001
mobility_index              -0.0238      0.020     -1.186      0.241      -0.064       0.016
containment_health_index     0.1211      0.050      2.406      0.019       0.020       0.222
democracy_index             -0.0109      0.023     -0.468      0.641      -0.058       0.036
distance_log                 1.5452      1.005      1.538      0.130      -0.466       3.557
individualism_gov           -0.0002      0.001     -0.223      0.824      -0.002       0.002
cases_neighbors              0.0013      0.003      0.409      0.684      -0.005       0.008
==============================================================================
Omnibus:                       54.858   Durbin-Watson:                   1.952
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              376.731
Skew:                          -2.058   Prob(JB):                     1.56e-82
Kurtosis:                      13.423   Cond. No.                     1.26e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.26e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- MONTH: 8 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.502
Model:                                OLS   Adj. R-squared:                  0.380
Method:                     Least Squares   F-statistic:                     4.112
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           6.75e-05
Time:                            15:04:27   Log-Likelihood:                -148.60
No. Observations:                      72   AIC:                             327.2
Df Residuals:                          57   BIC:                             361.3
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -28.0291      9.325     -3.006      0.004     -46.702      -9.356
continent[T.AS]              4.0171      1.415      2.839      0.006       1.184       6.851
continent[T.EU]              4.3473      1.106      3.930      0.000       2.132       6.563
continent[T.N.A.]            1.9246      1.285      1.498      0.140      -0.648       4.498
continent[T.OC]              0.7637      1.949      0.392      0.697      -3.139       4.666
continent[T.SA]              1.3112      1.795      0.731      0.468      -2.283       4.905
individualism_index          0.0614      0.065      0.938      0.352      -0.070       0.192
gdp_per_capita           -1.748e-05   1.75e-05     -0.999      0.322   -5.25e-05    1.76e-05
population_density           0.0004      0.000      1.252      0.216      -0.000       0.001
mobility_index              -0.0077      0.017     -0.462      0.646      -0.041       0.026
containment_health_index     0.1360      0.049      2.793      0.007       0.038       0.234
democracy_index              0.0149      0.022      0.676      0.502      -0.029       0.059
distance_log                 2.1582      0.950      2.271      0.027       0.255       4.061
individualism_gov           -0.0008      0.001     -0.766      0.447      -0.003       0.001
cases_neighbors              0.0009      0.003      0.320      0.750      -0.005       0.007
==============================================================================
Omnibus:                       56.594   Durbin-Watson:                   1.892
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              411.709
Skew:                          -2.120   Prob(JB):                     3.97e-90
Kurtosis:                      13.920   Cond. No.                     1.27e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.27e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- MONTH: 9 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.599
Model:                                OLS   Adj. R-squared:                  0.501
Method:                     Least Squares   F-statistic:                     6.082
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           3.85e-07
Time:                            15:04:27   Log-Likelihood:                -142.87
No. Observations:                      72   AIC:                             315.7
Df Residuals:                          57   BIC:                             349.9
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -31.0789      8.626     -3.603      0.001     -48.352     -13.806
continent[T.AS]              4.3768      1.343      3.259      0.002       1.688       7.066
continent[T.EU]              4.9054      0.994      4.935      0.000       2.915       6.896
continent[T.N.A.]            1.7243      1.149      1.501      0.139      -0.576       4.024
continent[T.OC]             -0.2881      1.781     -0.162      0.872      -3.855       3.279
continent[T.SA]              1.3408      1.393      0.962      0.340      -1.449       4.131
individualism_index          0.0727      0.057      1.274      0.208      -0.042       0.187
gdp_per_capita           -7.089e-06   1.62e-05     -0.438      0.663   -3.95e-05    2.54e-05
population_density        7.236e-05      0.000      0.261      0.795      -0.000       0.001
mobility_index              -0.0125      0.023     -0.549      0.585      -0.058       0.033
containment_health_index     0.1366      0.046      2.990      0.004       0.045       0.228
democracy_index              0.0083      0.021      0.406      0.687      -0.033       0.050
distance_log                 2.5093      0.893      2.811      0.007       0.722       4.297
individualism_gov           -0.0010      0.001     -1.028      0.309      -0.003       0.001
cases_neighbors              0.0015      0.002      0.829      0.411      -0.002       0.005
==============================================================================
Omnibus:                       63.478   Durbin-Watson:                   1.803
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              540.896
Skew:                          -2.413   Prob(JB):                    3.52e-118
Kurtosis:                      15.531   Cond. No.                     1.27e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.27e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- MONTH: 10 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.680
Model:                                OLS   Adj. R-squared:                  0.601
Method:                     Least Squares   F-statistic:                     8.635
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           1.32e-09
Time:                            15:04:27   Log-Likelihood:                -140.89
No. Observations:                      72   AIC:                             311.8
Df Residuals:                          57   BIC:                             345.9
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -31.9953      8.435     -3.793      0.000     -48.886     -15.105
continent[T.AS]              4.2210      1.357      3.110      0.003       1.503       6.939
continent[T.EU]              5.5574      1.018      5.461      0.000       3.520       7.595
continent[T.N.A.]            2.6310      1.069      2.461      0.017       0.491       4.771
continent[T.OC]             -0.4809      1.719     -0.280      0.781      -3.922       2.961
continent[T.SA]              1.7679      1.292      1.369      0.176      -0.818       4.354
individualism_index          0.1283      0.055      2.352      0.022       0.019       0.238
gdp_per_capita           -9.235e-06   1.63e-05     -0.565      0.574    -4.2e-05    2.35e-05
population_density          -0.0001      0.000     -0.424      0.673      -0.001       0.000
mobility_index               0.0019      0.023      0.082      0.935      -0.044       0.047
containment_health_index     0.1805      0.046      3.949      0.000       0.089       0.272
democracy_index              0.0040      0.020      0.197      0.845      -0.036       0.044
distance_log                 2.4402      0.888      2.748      0.008       0.662       4.218
individualism_gov           -0.0020      0.001     -2.147      0.036      -0.004      -0.000
cases_neighbors              0.0004      0.001      0.414      0.681      -0.002       0.002
==============================================================================
Omnibus:                       56.865   Durbin-Watson:                   1.731
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              438.806
Skew:                          -2.103   Prob(JB):                     5.18e-96
Kurtosis:                      14.339   Cond. No.                     1.28e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.28e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- MONTH: 11 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.719
Model:                                OLS   Adj. R-squared:                  0.650
Method:                     Least Squares   F-statistic:                     10.42
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           4.25e-11
Time:                            15:04:27   Log-Likelihood:                -138.88
No. Observations:                      72   AIC:                             307.8
Df Residuals:                          57   BIC:                             341.9
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -31.1961      8.159     -3.823      0.000     -47.534     -14.858
continent[T.AS]              3.7483      1.344      2.790      0.007       1.058       6.439
continent[T.EU]              4.5439      1.220      3.725      0.000       2.102       6.986
continent[T.N.A.]            3.0366      1.069      2.842      0.006       0.897       5.177
continent[T.OC]             -2.4472      1.901     -1.287      0.203      -6.254       1.359
continent[T.SA]              2.0639      1.250      1.652      0.104      -0.439       4.566
individualism_index          0.2274      0.066      3.422      0.001       0.094       0.361
gdp_per_capita           -5.254e-06   1.55e-05     -0.340      0.735   -3.62e-05    2.57e-05
population_density          -0.0002      0.000     -0.848      0.400      -0.001       0.000
mobility_index               0.0359      0.027      1.322      0.191      -0.018       0.090
containment_health_index     0.2481      0.049      5.056      0.000       0.150       0.346
democracy_index             -0.0060      0.020     -0.298      0.767      -0.046       0.034
distance_log                 2.0746      0.856      2.423      0.019       0.360       3.789
individualism_gov           -0.0037      0.001     -3.368      0.001      -0.006      -0.001
cases_neighbors              0.0011      0.001      1.589      0.118      -0.000       0.002
==============================================================================
Omnibus:                       55.799   Durbin-Watson:                   1.935
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              414.083
Skew:                          -2.067   Prob(JB):                     1.21e-90
Kurtosis:                      13.997   Cond. No.                     1.28e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.28e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- MONTH: 12 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.624
Model:                                OLS   Adj. R-squared:                  0.532
Method:                     Least Squares   F-statistic:                     6.769
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           7.54e-08
Time:                            15:04:27   Log-Likelihood:                -145.85
No. Observations:                      72   AIC:                             321.7
Df Residuals:                          57   BIC:                             355.9
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -30.5457      9.084     -3.363      0.001     -48.736     -12.356
continent[T.AS]              3.3357      1.480      2.254      0.028       0.372       6.299
continent[T.EU]              3.3807      1.360      2.485      0.016       0.656       6.105
continent[T.N.A.]            1.8079      1.243      1.455      0.151      -0.681       4.297
continent[T.OC]             -2.8923      2.036     -1.420      0.161      -6.970       1.185
continent[T.SA]              1.2758      1.416      0.901      0.371      -1.559       4.111
individualism_index          0.1922      0.074      2.596      0.012       0.044       0.340
gdp_per_capita           -2.454e-06   1.71e-05     -0.144      0.886   -3.66e-05    3.17e-05
population_density          -0.0002      0.000     -0.751      0.455      -0.001       0.000
mobility_index               0.0171      0.030      0.563      0.575      -0.044       0.078
containment_health_index     0.2049      0.054      3.814      0.000       0.097       0.312
democracy_index           3.136e-05      0.022      0.001      0.999      -0.044       0.044
distance_log                 2.2504      0.915      2.459      0.017       0.418       4.083
individualism_gov           -0.0030      0.001     -2.487      0.016      -0.005      -0.001
cases_neighbors              0.0011      0.001      1.394      0.169      -0.000       0.003
==============================================================================
Omnibus:                       64.311   Durbin-Watson:                   2.066
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              581.013
Skew:                          -2.426   Prob(JB):                    6.83e-127
Kurtosis:                      16.043   Cond. No.                     1.29e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.29e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

result_dict.keys()

dict_keys(['2_pvalues', '2_params', '3_pvalues', '3_params', '4_pvalues', '4_params', '5_pvalues', '5_params', '6_pvalues', '6_params', '7_pvalues', '7_params', '8_pvalues', '8_params', '9_pvalues', '9_params', '10_pvalues', '10_params', '11_pvalues', '11_params', '12_pvalues', '12_params'])

pvalues_df = pd.DataFrame()
coeff_df = pd.DataFrame()

for key in result_dict.keys():
    if '_pvalues' in key:
        result_series = result_dict[key]
        pvalues_df = pvalues_df.append(result_series, ignore_index=True)
        
    if '_params' in key:
        params_series = result_dict[key]
        coeff_df = coeff_df.append(params_series, ignore_index=True)

pvalues_df.index = range(2,13)
coeff_df.index = range(2,13)

5.3. Regression for different seasons

5.3.1. Regression model summaries

seasons_dict = {'2': 'winter_1',
                '3': 'spring',
                '4': 'spring',
                '5': 'spring',
                '6': 'summer',
                '7': 'summer',
                '8': 'summer',
                '9': 'autumn',
                '10': 'autumn',
                '11': 'autumn',
                '12': 'winter_2'}

seasons_dict = {int(k):v for k,v in seasons_dict.items()}

df['season'] = df['month'].map(seasons_dict)

vars_to_agg = ['individualism_index', 'health_expenditure', 'gdp_per_capita', 'over65_per_capita',
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log',  'individualism_gov', 'cases_neighbors']

dict_for_agg = {v:'mean' for v in vars_to_agg}
dict_for_agg.update({'new_cases_per_100k': 'sum'})

df_seasons = df.groupby(['country', 'season', 'continent']).agg(dict_for_agg).reset_index()
df_seasons['new_cases_per_100k_log'] = np.log(df_seasons['new_cases_per_100k'] + 0.0000000001)

df_seasons = df_seasons.set_index('country')

from statsmodels.iolib.summary2 import summary_col

df.season.unique()

array(['winter_1', 'spring', 'summer', 'autumn', 'winter_2'], dtype=object)

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'continent',  'individualism_gov', 'cases_neighbors']

results1 = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[df_seasons.season == 'winter_1']).fit()
results2 = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[df_seasons.season == 'spring']).fit()
results3 = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[df_seasons.season == 'summer']).fit()
results4 = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[df_seasons.season == 'autumn']).fit()
results5 = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[df_seasons.season == 'winter_2']).fit()

def get_season_vars(with_tanzania=True):
    season_vars = {}
    vars_to_use = ['individualism_index', 'gdp_per_capita', 
                   'population_density', 
                   'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'continent',  'individualism_gov',
                  'cases_neighbors']

    if with_tanzania:
        for season in ['winter_1', 'spring', 'summer', 'autumn', 'winter_2']:
            results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[df_seasons['season'] == season]).fit()
            season_vars['{}'.format(season)] = results
            
    else:
        for season in ['winter_1', 'spring', 'summer', 'autumn', 'winter_2']:
            results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[
                (df_seasons['season'] == season) & (df_seasons.index != 'Tanzania')]).fit()
            season_vars['{}'.format(season)] = results
        
    return season_vars

season_vars = get_season_vars(with_tanzania=False)

season_vars

{'winter_1': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2198e28a7f0>,
 'spring': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2198e299ca0>,
 'summer': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2198dfedd00>,
 'autumn': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2198e2b2cd0>,
 'winter_2': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2198e2bf4f0>}

5.3.2. Regression model summaries with robust standard errors and without Tanzania

season_vars2 = get_season_vars(with_tanzania=False)
season_vars2['cumulative'] = results_total2

keys_list = list(season_vars2.keys())
keys_list.insert(0, keys_list.pop())
season_vars2 = dict(sorted(season_vars2.items(), key = lambda pair: keys_list.index(pair[0])))

for key, value in season_vars2.items():
    season_vars2[key] = value.get_robustcov_results()

season_vars2

{'cumulative': <statsmodels.regression.linear_model.OLSResults at 0x2299ae475b0>,
 'winter_1': <statsmodels.regression.linear_model.OLSResults at 0x2299dd05b80>,
 'spring': <statsmodels.regression.linear_model.OLSResults at 0x2299d5322b0>,
 'summer': <statsmodels.regression.linear_model.OLSResults at 0x2299d8a6d60>,
 'autumn': <statsmodels.regression.linear_model.OLSResults at 0x2299d534040>,
 'winter_2': <statsmodels.regression.linear_model.OLSResults at 0x2299d9401f0>}

rs_list = list(season_vars2.values())[1:]
result_summ = summary_col(rs_list, stars=True)

res_df = result_summ.tables[0]
res_df.columns = ['Winter1', 'Spring', 'Summer', 'Autumn', 'Winter2']

res_df

	Cumulative
Intercept	1.8644
	(7.4468)
continent[T.AS]	2.0664*
	(1.1091)
continent[T.EU]	1.4363
	(0.9978)
continent[T.N.A.]	0.5697
	(0.9854)
continent[T.OC]	-2.6646*
	(1.4573)
continent[T.SA]	1.8619
	(1.1143)
individualism_index	-0.0606
	(0.0700)
gdp_per_capita	-0.0000
	(0.0000)
population_density	-0.0001
	(0.0002)
mobility_index_avg	0.0047
	(0.0243)
containment_health_index_avg	0.0180
	(0.0622)
democracy_index	-0.0109
	(0.0164)
distance_log	0.8620
	(0.7133)
individualism_gov	0.0018
	(0.0013)
cases_neighbors	0.0002
	(0.0006)
R-squared	0.4704
R-squared Adj.	0.3380

with open('summary_seasonal.tex','w') as tf:
    tf.write(res_df.to_latex())

5.3.3. Regression models with Tanzania

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'continent',  'individualism_gov', 'cases_neighbors']

for season in df.season.unique():
    
    results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[df_seasons.season == season]).fit()
    print(f"\n\n------------------- Season: {season} -----------------------")
    print(results.summary())
    
season_vars = get_season_vars(with_tanzania=False)

------------------- Season: winter_1 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.414
Model:                                OLS   Adj. R-squared:                  0.270
Method:                     Least Squares   F-statistic:                     2.879
Date:                    Tue, 05 Jan 2021   Prob (F-statistic):            0.00246
Time:                            22:57:08   Log-Likelihood:                -248.22
No. Observations:                      72   AIC:                             526.4
Df Residuals:                          57   BIC:                             560.6
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                   76.3746     43.976      1.737      0.088     -11.687     164.436
continent[T.AS]             -5.0514      6.038     -0.837      0.406     -17.141       7.039
continent[T.EU]             -2.1679      4.455     -0.487      0.628     -11.089       6.753
continent[T.N.A.]            1.3849      4.750      0.292      0.772      -8.127      10.896
continent[T.OC]             -1.5500      8.220     -0.189      0.851     -18.010      14.910
continent[T.SA]              2.7905      5.719      0.488      0.627      -8.662      14.243
individualism_index          0.0237      0.098      0.241      0.810      -0.173       0.220
gdp_per_capita            9.923e-05   7.31e-05      1.358      0.180   -4.71e-05       0.000
population_density           0.0005      0.001      0.441      0.661      -0.002       0.003
mobility_index               0.1675      0.282      0.593      0.556      -0.398       0.733
containment_health_index    -0.1867      0.301     -0.620      0.538      -0.789       0.416
democracy_index              0.0136      0.094      0.145      0.886      -0.175       0.203
distance_log               -10.4792      4.558     -2.299      0.025     -19.606      -1.352
individualism_gov            0.0079      0.006      1.298      0.200      -0.004       0.020
cases_neighbors              1.5541      3.923      0.396      0.693      -6.301       9.409
==============================================================================
Omnibus:                        3.002   Durbin-Watson:                   2.651
Prob(Omnibus):                  0.223   Jarque-Bera (JB):                1.705
Skew:                           0.026   Prob(JB):                        0.426
Kurtosis:                       2.248   Cond. No.                     1.50e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.5e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: spring -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.656
Model:                                OLS   Adj. R-squared:                  0.571
Method:                     Least Squares   F-statistic:                     7.761
Date:                    Tue, 05 Jan 2021   Prob (F-statistic):           8.21e-09
Time:                            22:57:08   Log-Likelihood:                -97.796
No. Observations:                      72   AIC:                             225.6
Df Residuals:                          57   BIC:                             259.7
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                   -6.9245      5.183     -1.336      0.187     -17.304       3.455
continent[T.AS]              1.5335      0.743      2.064      0.044       0.046       3.021
continent[T.EU]              2.1367      0.523      4.085      0.000       1.089       3.184
continent[T.N.A.]            1.2364      0.587      2.108      0.039       0.062       2.411
continent[T.OC]             -0.1233      0.990     -0.124      0.901      -2.107       1.860
continent[T.SA]              1.7343      0.703      2.467      0.017       0.327       3.142
individualism_index          0.0125      0.049      0.256      0.799      -0.085       0.110
gdp_per_capita            2.505e-05   9.28e-06      2.700      0.009    6.47e-06    4.36e-05
population_density           0.0003      0.000      1.956      0.055   -7.08e-06       0.001
mobility_index              -0.0205      0.015     -1.370      0.176      -0.050       0.009
containment_health_index    -0.0100      0.033     -0.299      0.766      -0.077       0.057
democracy_index             -0.0148      0.011     -1.336      0.187      -0.037       0.007
distance_log                 1.0111      0.511      1.980      0.053      -0.012       2.034
individualism_gov        -6.548e-06      0.001     -0.008      0.994      -0.002       0.002
cases_neighbors              0.0024      0.004      0.623      0.536      -0.005       0.010
==============================================================================
Omnibus:                        2.079   Durbin-Watson:                   1.427
Prob(Omnibus):                  0.354   Jarque-Bera (JB):                1.643
Skew:                          -0.368   Prob(JB):                        0.440
Kurtosis:                       3.074   Cond. No.                     1.43e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.43e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: summer -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.423
Model:                                OLS   Adj. R-squared:                  0.282
Method:                     Least Squares   F-statistic:                     2.991
Date:                    Tue, 05 Jan 2021   Prob (F-statistic):            0.00176
Time:                            22:57:08   Log-Likelihood:                -176.08
No. Observations:                      72   AIC:                             382.2
Df Residuals:                          57   BIC:                             416.3
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -27.1022     13.886     -1.952      0.056     -54.908       0.704
continent[T.AS]              4.1260      2.140      1.928      0.059      -0.160       8.411
continent[T.EU]              5.1252      1.608      3.188      0.002       1.906       8.345
continent[T.N.A.]            2.2478      1.952      1.152      0.254      -1.660       6.156
continent[T.OC]              2.4160      2.894      0.835      0.407      -3.379       8.211
continent[T.SA]              1.6003      2.785      0.575      0.568      -3.976       7.176
individualism_index          0.0784      0.103      0.763      0.449      -0.127       0.284
gdp_per_capita            1.223e-05    2.6e-05      0.469      0.641   -3.99e-05    6.44e-05
population_density           0.0002      0.000      0.539      0.592      -0.001       0.001
mobility_index              -0.0060      0.029     -0.206      0.837      -0.064       0.052
containment_health_index     0.2036      0.075      2.713      0.009       0.053       0.354
democracy_index             -0.0033      0.033     -0.102      0.919      -0.069       0.062
distance_log                 1.7596      1.417      1.242      0.219      -1.077       4.596
individualism_gov           -0.0013      0.002     -0.802      0.426      -0.005       0.002
cases_neighbors              0.0019      0.006      0.346      0.731      -0.009       0.013
==============================================================================
Omnibus:                       91.401   Durbin-Watson:                   1.897
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1778.080
Skew:                          -3.649   Prob(JB):                         0.00
Kurtosis:                      26.226   Cond. No.                     1.29e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.29e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: autumn -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.595
Model:                                OLS   Adj. R-squared:                  0.495
Method:                     Least Squares   F-statistic:                     5.977
Date:                    Tue, 05 Jan 2021   Prob (F-statistic):           4.97e-07
Time:                            22:57:08   Log-Likelihood:                -168.86
No. Observations:                      72   AIC:                             367.7
Df Residuals:                          57   BIC:                             401.9
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -37.2632     12.524     -2.975      0.004     -62.343     -12.183
continent[T.AS]              4.6602      2.021      2.306      0.025       0.614       8.706
continent[T.EU]              5.6948      1.664      3.423      0.001       2.363       9.027
continent[T.N.A.]            3.2374      1.627      1.989      0.051      -0.022       6.496
continent[T.OC]              0.5475      2.576      0.213      0.832      -4.611       5.706
continent[T.SA]              2.4500      1.939      1.263      0.212      -1.433       6.333
individualism_index          0.2448      0.095      2.574      0.013       0.054       0.435
gdp_per_capita           -8.304e-06   2.35e-05     -0.354      0.725   -5.53e-05    3.87e-05
population_density       -4.507e-05      0.000     -0.114      0.910      -0.001       0.001
mobility_index               0.0389      0.038      1.024      0.310      -0.037       0.115
containment_health_index     0.3267      0.074      4.422      0.000       0.179       0.475
democracy_index             -0.0029      0.030     -0.096      0.924      -0.063       0.057
distance_log                 2.2470      1.314      1.710      0.093      -0.384       4.878
individualism_gov           -0.0041      0.002     -2.550      0.013      -0.007      -0.001
cases_neighbors              0.0014      0.002      0.819      0.416      -0.002       0.005
==============================================================================
Omnibus:                       79.610   Durbin-Watson:                   1.974
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1148.897
Skew:                          -3.064   Prob(JB):                    3.31e-250
Kurtosis:                      21.586   Cond. No.                     1.29e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.29e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: winter_2 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.547
Model:                                OLS   Adj. R-squared:                  0.435
Method:                     Least Squares   F-statistic:                     4.909
Date:                    Tue, 05 Jan 2021   Prob (F-statistic):           7.62e-06
Time:                            22:57:08   Log-Likelihood:                -171.08
No. Observations:                      72   AIC:                             372.2
Df Residuals:                          57   BIC:                             406.3
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -37.5908     12.896     -2.915      0.005     -63.414     -11.768
continent[T.AS]              3.9128      2.101      1.863      0.068      -0.294       8.119
continent[T.EU]              4.1091      1.931      2.128      0.038       0.242       7.977
continent[T.N.A.]            2.6432      1.765      1.498      0.140      -0.890       6.177
continent[T.OC]             -2.1184      2.891     -0.733      0.467      -7.907       3.670
continent[T.SA]              1.8784      2.010      0.935      0.354      -2.146       5.903
individualism_index          0.2750      0.105      2.617      0.011       0.065       0.486
gdp_per_capita             1.95e-06   2.42e-05      0.081      0.936   -4.65e-05    5.04e-05
population_density          -0.0002      0.000     -0.553      0.583      -0.001       0.001
mobility_index               0.0461      0.043      1.071      0.289      -0.040       0.132
containment_health_index     0.3122      0.076      4.095      0.000       0.160       0.465
democracy_index             -0.0116      0.031     -0.371      0.712      -0.074       0.051
distance_log                 2.3637      1.299      1.819      0.074      -0.238       4.966
individualism_gov           -0.0044      0.002     -2.586      0.012      -0.008      -0.001
cases_neighbors              0.0014      0.001      1.269      0.210      -0.001       0.004
==============================================================================
Omnibus:                       80.030   Durbin-Watson:                   2.131
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1153.113
Skew:                          -3.091   Prob(JB):                    4.03e-251
Kurtosis:                      21.605   Cond. No.                     1.29e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.29e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

5.3.4. Without Tanzania

5.3.4.1. No continents

def get_season_vars(with_tanzania=True, vars_to_use = ['individualism_index', 'gdp_per_capita', 
                   'population_density', 
                   'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'continent',  'individualism_gov',
                  'cases_neighbors']):
    season_vars = {}
    
    if with_tanzania:
        for season in ['winter_1', 'spring', 'summer', 'autumn', 'winter_2']:
            results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[df_seasons['season'] == season]).fit()
            season_vars['{}'.format(season)] = results
            
    else:
        for season in ['winter_1', 'spring', 'summer', 'autumn', 'winter_2']:
            results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[
                (df_seasons['season'] == season) & (df_seasons.index != 'Tanzania')]).fit()
            season_vars['{}'.format(season)] = results
        
    return season_vars

season_vars = get_season_vars(with_tanzania=False, vars_to_use = ['individualism_index', 'gdp_per_capita', 
                   'population_density', 
                   'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'individualism_gov',
                  'cases_neighbors'])

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index_avg', 'containment_health_index_avg', 'democracy_index', 'distance_log', 'individualism_gov', 'cases_neighbors']
results_total_no_continent = smf.ols('confirmed_log ~ ' + ' + '.join(vars_to_use), data = df_newest[df_newest != 'Tanzania']).fit()

season_vars['cumulative'] = results_total_no_continent
keys_list = list(season_vars.keys())
keys_list.insert(0, keys_list.pop())
season_vars = dict(sorted(season_vars.items(), key = lambda pair: keys_list.index(pair[0])))

rs_list = list(season_vars.values())
result_summ = summary_col(rs_list, stars=True)

table_nocont = result_summ.tables[0]
table_nocont.columns = ['cumulative', 'winter_1', 'spring', 'summer', 'autumn', 'winter_2']

with open('no_continent_reg.tex','w') as tf:
    tf.write(table_nocont.to_latex())

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log',  'individualism_gov', 'cases_neighbors']

for season in df.season.unique():
    
    results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[(df_seasons.season == season) & (df_seasons.index != 'Tanzania')]).fit()
    print(f"\n\n------------------- Season: {season} -----------------------")
    print(results.summary())

------------------- Season: winter_1 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.397
Model:                                OLS   Adj. R-squared:                  0.308
Method:                     Least Squares   F-statistic:                     4.468
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           0.000159
Time:                            18:59:03   Log-Likelihood:                -245.75
No. Observations:                      71   AIC:                             511.5
Df Residuals:                          61   BIC:                             534.1
Df Model:                               9                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                   39.5698     22.780      1.737      0.087      -5.981      85.121
individualism_index          0.0147      0.093      0.157      0.876      -0.172       0.201
gdp_per_capita            7.487e-05    6.6e-05      1.134      0.261   -5.71e-05       0.000
population_density           0.0005      0.001      0.406      0.686      -0.002       0.003
mobility_index               0.0419      0.242      0.173      0.863      -0.441       0.525
containment_health_index    -0.2079      0.285     -0.729      0.469      -0.778       0.362
democracy_index              0.0427      0.081      0.526      0.601      -0.120       0.205
distance_log                -6.6397      2.374     -2.797      0.007     -11.387      -1.893
individualism_gov            0.0081      0.006      1.425      0.159      -0.003       0.019
cases_neighbors              2.2339      3.683      0.607      0.546      -5.131       9.599
==============================================================================
Omnibus:                        3.643   Durbin-Watson:                   2.563
Prob(Omnibus):                  0.162   Jarque-Bera (JB):                1.893
Skew:                           0.033   Prob(JB):                        0.388
Kurtosis:                       2.203   Cond. No.                     7.95e+05
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 7.95e+05. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: spring -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.539
Model:                                OLS   Adj. R-squared:                  0.471
Method:                     Least Squares   F-statistic:                     7.937
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           1.18e-07
Time:                            18:59:03   Log-Likelihood:                -103.59
No. Observations:                      71   AIC:                             227.2
Df Residuals:                          61   BIC:                             249.8
Df Model:                               9                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                   -2.0597      3.226     -0.638      0.526      -8.511       4.392
individualism_index         -0.0144      0.051     -0.281      0.780      -0.117       0.088
gdp_per_capita            2.562e-05   9.55e-06      2.684      0.009    6.53e-06    4.47e-05
population_density           0.0003      0.000      1.835      0.071   -2.62e-05       0.001
mobility_index              -0.0121      0.015     -0.833      0.408      -0.041       0.017
containment_health_index    -0.0328      0.036     -0.910      0.366      -0.105       0.039
democracy_index             -0.0062      0.011     -0.584      0.561      -0.027       0.015
distance_log                 0.7522      0.274      2.742      0.008       0.204       1.301
individualism_gov            0.0003      0.001      0.372      0.711      -0.001       0.002
cases_neighbors              0.0097      0.003      2.780      0.007       0.003       0.017
==============================================================================
Omnibus:                        0.796   Durbin-Watson:                   1.153
Prob(Omnibus):                  0.672   Jarque-Bera (JB):                0.908
Skew:                          -0.208   Prob(JB):                        0.635
Kurtosis:                       2.634   Cond. No.                     8.31e+05
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 8.31e+05. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: summer -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.412
Model:                                OLS   Adj. R-squared:                  0.326
Method:                     Least Squares   F-statistic:                     4.756
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           8.30e-05
Time:                            18:59:03   Log-Likelihood:                -120.12
No. Observations:                      71   AIC:                             260.2
Df Residuals:                          61   BIC:                             282.9
Df Model:                               9                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                   -7.7390      3.627     -2.133      0.037     -14.992      -0.485
individualism_index         -0.0444      0.046     -0.968      0.337      -0.136       0.047
gdp_per_capita            1.818e-05   1.15e-05      1.583      0.119   -4.79e-06    4.11e-05
population_density           0.0002      0.000      1.123      0.266      -0.000       0.001
mobility_index               0.0015      0.010      0.148      0.883      -0.019       0.022
containment_health_index     0.0258      0.036      0.722      0.473      -0.046       0.097
democracy_index             -0.0032      0.013     -0.237      0.813      -0.030       0.024
distance_log                 1.2309      0.360      3.422      0.001       0.512       1.950
individualism_gov            0.0006      0.001      0.848      0.400      -0.001       0.002
cases_neighbors              0.0015      0.002      0.822      0.414      -0.002       0.005
==============================================================================
Omnibus:                        7.740   Durbin-Watson:                   1.691
Prob(Omnibus):                  0.021   Jarque-Bera (JB):                7.137
Skew:                          -0.737   Prob(JB):                       0.0282
Kurtosis:                       3.490   Cond. No.                     7.41e+05
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 7.41e+05. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: autumn -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.576
Model:                                OLS   Adj. R-squared:                  0.513
Method:                     Least Squares   F-statistic:                     9.196
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           1.20e-08
Time:                            18:59:03   Log-Likelihood:                -121.67
No. Observations:                      71   AIC:                             263.3
Df Residuals:                          61   BIC:                             286.0
Df Model:                               9                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                   -6.7117      3.740     -1.795      0.078     -14.190       0.766
individualism_index          0.0600      0.049      1.216      0.229      -0.039       0.159
gdp_per_capita           -6.628e-06   1.18e-05     -0.562      0.576   -3.02e-05     1.7e-05
population_density       -6.633e-05      0.000     -0.329      0.743      -0.000       0.000
mobility_index              -0.0130      0.018     -0.712      0.479      -0.049       0.023
containment_health_index     0.0554      0.042      1.312      0.194      -0.029       0.140
democracy_index              0.0128      0.014      0.905      0.369      -0.015       0.041
distance_log                 0.7360      0.345      2.132      0.037       0.046       1.426
individualism_gov           -0.0008      0.001     -0.994      0.324      -0.003       0.001
cases_neighbors              0.0039      0.001      6.298      0.000       0.003       0.005
==============================================================================
Omnibus:                       10.455   Durbin-Watson:                   1.553
Prob(Omnibus):                  0.005   Jarque-Bera (JB):               10.463
Skew:                          -0.900   Prob(JB):                      0.00535
Kurtosis:                       3.544   Cond. No.                     7.48e+05
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 7.48e+05. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: winter_2 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.590
Model:                                OLS   Adj. R-squared:                  0.530
Method:                     Least Squares   F-statistic:                     9.766
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           4.46e-09
Time:                            18:59:03   Log-Likelihood:                -118.09
No. Observations:                      71   AIC:                             256.2
Df Residuals:                          61   BIC:                             278.8
Df Model:                               9                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                   -3.4210      3.697     -0.925      0.358     -10.814       3.972
individualism_index         -0.0293      0.047     -0.624      0.535      -0.123       0.065
gdp_per_capita           -3.149e-06    1.1e-05     -0.286      0.776   -2.52e-05    1.89e-05
population_density          -0.0002      0.000     -1.037      0.304      -0.001       0.000
mobility_index              -0.0490      0.020     -2.468      0.016      -0.089      -0.009
containment_health_index    -0.0090      0.040     -0.224      0.823      -0.089       0.071
democracy_index              0.0136      0.014      1.006      0.318      -0.013       0.041
distance_log                 0.7082      0.310      2.284      0.026       0.088       1.328
individualism_gov            0.0006      0.001      0.797      0.429      -0.001       0.002
cases_neighbors              0.0015      0.000      3.787      0.000       0.001       0.002
==============================================================================
Omnibus:                       16.188   Durbin-Watson:                   1.626
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               19.847
Skew:                          -1.018   Prob(JB):                     4.90e-05
Kurtosis:                       4.600   Cond. No.                     7.78e+05
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 7.78e+05. This might indicate that there are
strong multicollinearity or other numerical problems.

5.3.4.2. Continents

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'continent',  'individualism_gov', 'cases_neighbors']

for season in df.season.unique():
    
    results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[(df_seasons.season == season) & (df_seasons.index != 'Tanzania')]).fit()
    print(f"\n\n------------------- Season: {season} -----------------------")
    print(results.summary())

------------------- Season: winter_1 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.409
Model:                                OLS   Adj. R-squared:                  0.262
Method:                     Least Squares   F-statistic:                     2.772
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):            0.00347
Time:                            14:02:06   Log-Likelihood:                -245.04
No. Observations:                      71   AIC:                             520.1
Df Residuals:                          56   BIC:                             554.0
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                   78.6516     44.384      1.772      0.082     -10.261     167.564
continent[T.AS]             -5.8156      6.202     -0.938      0.352     -18.240       6.609
continent[T.EU]             -2.8400      4.616     -0.615      0.541     -12.088       6.408
continent[T.N.A.]            0.7481      4.892      0.153      0.879      -9.051      10.547
continent[T.OC]             -2.2508      8.347     -0.270      0.788     -18.973      14.471
continent[T.SA]              2.1283      5.855      0.363      0.718      -9.601      13.858
individualism_index          0.0179      0.099      0.181      0.857      -0.181       0.217
gdp_per_capita            9.956e-05   7.35e-05      1.355      0.181   -4.76e-05       0.000
population_density           0.0005      0.001      0.439      0.662      -0.002       0.003
mobility_index               0.1595      0.284      0.561      0.577      -0.410       0.729
containment_health_index    -0.2044      0.304     -0.672      0.504      -0.814       0.405
democracy_index              0.0152      0.095      0.160      0.874      -0.175       0.205
distance_log               -10.6357      4.591     -2.317      0.024     -19.832      -1.439
individualism_gov            0.0082      0.006      1.340      0.185      -0.004       0.021
cases_neighbors              1.5346      3.945      0.389      0.699      -6.368       9.437
==============================================================================
Omnibus:                        3.442   Durbin-Watson:                   2.625
Prob(Omnibus):                  0.179   Jarque-Bera (JB):                1.828
Skew:                           0.013   Prob(JB):                        0.401
Kurtosis:                       2.214   Cond. No.                     1.51e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.51e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: spring -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.651
Model:                                OLS   Adj. R-squared:                  0.564
Method:                     Least Squares   F-statistic:                     7.462
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           1.81e-08
Time:                            14:02:06   Log-Likelihood:                -93.742
No. Observations:                      71   AIC:                             217.5
Df Residuals:                          56   BIC:                             251.4
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                   -4.9634      5.072     -0.979      0.332     -15.124       5.197
continent[T.AS]              1.2910      0.724      1.783      0.080      -0.160       2.742
continent[T.EU]              1.8514      0.520      3.564      0.001       0.811       2.892
continent[T.N.A.]            1.0195      0.574      1.777      0.081      -0.130       2.169
continent[T.OC]             -0.3414      0.960     -0.356      0.723      -2.264       1.582
continent[T.SA]              1.5059      0.685      2.198      0.032       0.133       2.879
individualism_index         -0.0083      0.048     -0.173      0.863      -0.104       0.088
gdp_per_capita            2.468e-05   8.95e-06      2.757      0.008    6.75e-06    4.26e-05
population_density           0.0003      0.000      2.043      0.046    5.84e-06       0.001
mobility_index              -0.0208      0.014     -1.440      0.155      -0.050       0.008
containment_health_index    -0.0345      0.034     -1.017      0.313      -0.102       0.033
democracy_index             -0.0141      0.011     -1.321      0.192      -0.036       0.007
distance_log                 0.9754      0.493      1.979      0.053      -0.012       1.963
individualism_gov            0.0003      0.001      0.423      0.674      -0.001       0.002
cases_neighbors              0.0027      0.004      0.727      0.470      -0.005       0.010
==============================================================================
Omnibus:                        2.093   Durbin-Watson:                   1.339
Prob(Omnibus):                  0.351   Jarque-Bera (JB):                1.770
Skew:                          -0.387   Prob(JB):                        0.413
Kurtosis:                       2.983   Cond. No.                     1.45e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.45e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: summer -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.523
Model:                                OLS   Adj. R-squared:                  0.404
Method:                     Least Squares   F-statistic:                     4.388
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           3.33e-05
Time:                            14:02:07   Log-Likelihood:                -112.70
No. Observations:                      71   AIC:                             255.4
Df Residuals:                          56   BIC:                             289.3
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -12.4994      5.966     -2.095      0.041     -24.451      -0.548
continent[T.AS]              1.5181      0.923      1.644      0.106      -0.331       3.367
continent[T.EU]              2.1529      0.707      3.044      0.004       0.736       3.570
continent[T.N.A.]            0.7208      0.834      0.864      0.391      -0.950       2.392
continent[T.OC]             -0.4823      1.242     -0.388      0.699      -2.971       2.006
continent[T.SA]              0.5209      1.184      0.440      0.662      -1.852       2.894
individualism_index         -0.0478      0.044     -1.079      0.285      -0.137       0.041
gdp_per_capita            1.235e-05   1.11e-05      1.117      0.269   -9.81e-06    3.45e-05
population_density           0.0002      0.000      1.041      0.302      -0.000       0.001
mobility_index              -0.0193      0.012     -1.568      0.122      -0.044       0.005
containment_health_index     0.0185      0.034      0.547      0.587      -0.049       0.086
democracy_index             -0.0050      0.014     -0.362      0.719      -0.033       0.023
distance_log                 1.6458      0.602      2.736      0.008       0.441       2.851
individualism_gov            0.0008      0.001      1.119      0.268      -0.001       0.002
cases_neighbors              0.0009      0.002      0.368      0.714      -0.004       0.006
==============================================================================
Omnibus:                        5.196   Durbin-Watson:                   2.134
Prob(Omnibus):                  0.074   Jarque-Bera (JB):                4.555
Skew:                          -0.609   Prob(JB):                        0.103
Kurtosis:                       3.235   Cond. No.                     1.31e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.31e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: autumn -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.793
Model:                                OLS   Adj. R-squared:                  0.741
Method:                     Least Squares   F-statistic:                     15.31
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           2.53e-14
Time:                            14:02:07   Log-Likelihood:                -96.215
No. Observations:                      71   AIC:                             222.4
Df Residuals:                          56   BIC:                             256.4
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -22.0467      4.731     -4.660      0.000     -31.524     -12.569
continent[T.AS]              3.2832      0.756      4.345      0.000       1.770       4.797
continent[T.EU]              3.4457      0.631      5.463      0.000       2.182       4.709
continent[T.N.A.]            1.0693      0.617      1.734      0.088      -0.166       2.304
continent[T.OC]             -2.2546      0.970     -2.324      0.024      -4.198      -0.311
continent[T.SA]              0.6305      0.728      0.866      0.390      -0.828       2.089
individualism_index          0.0417      0.037      1.128      0.264      -0.032       0.116
gdp_per_capita           -1.264e-05   8.74e-06     -1.447      0.153   -3.01e-05    4.86e-06
population_density       -7.432e-05      0.000     -0.504      0.616      -0.000       0.000
mobility_index              -0.0211      0.015     -1.452      0.152      -0.050       0.008
containment_health_index     0.0379      0.031      1.204      0.234      -0.025       0.101
democracy_index              0.0145      0.011      1.296      0.200      -0.008       0.037
distance_log                 2.3798      0.489      4.865      0.000       1.400       3.360
individualism_gov           -0.0004      0.001     -0.656      0.515      -0.002       0.001
cases_neighbors              0.0012      0.001      1.914      0.061   -5.57e-05       0.002
==============================================================================
Omnibus:                       14.665   Durbin-Watson:                   1.806
Prob(Omnibus):                  0.001   Jarque-Bera (JB):               18.577
Skew:                          -0.890   Prob(JB):                     9.25e-05
Kurtosis:                       4.764   Cond. No.                     1.31e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.31e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: winter_2 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.778
Model:                                OLS   Adj. R-squared:                  0.723
Method:                     Least Squares   F-statistic:                     14.05
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           1.52e-13
Time:                            14:02:07   Log-Likelihood:                -96.287
No. Observations:                      71   AIC:                             222.6
Df Residuals:                          56   BIC:                             256.5
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -17.4795      4.771     -3.663      0.001     -27.038      -7.921
continent[T.AS]              2.2654      0.764      2.967      0.004       0.736       3.795
continent[T.EU]              2.0299      0.706      2.876      0.006       0.616       3.444
continent[T.N.A.]            0.2587      0.649      0.399      0.692      -1.042       1.559
continent[T.OC]             -4.3276      1.050     -4.120      0.000      -6.432      -2.223
continent[T.SA]              0.1582      0.731      0.216      0.829      -1.307       1.623
individualism_index          0.0386      0.040      0.970      0.336      -0.041       0.118
gdp_per_capita           -1.062e-05   8.77e-06     -1.212      0.231   -2.82e-05    6.94e-06
population_density          -0.0002      0.000     -1.344      0.184      -0.000     9.7e-05
mobility_index              -0.0367      0.016     -2.279      0.026      -0.069      -0.004
containment_health_index     0.0058      0.032      0.183      0.855      -0.058       0.069
democracy_index              0.0216      0.011      1.893      0.064      -0.001       0.044
distance_log                 2.0404      0.470      4.344      0.000       1.099       2.981
individualism_gov           -0.0003      0.001     -0.535      0.595      -0.002       0.001
cases_neighbors              0.0005      0.000      1.237      0.221      -0.000       0.001
==============================================================================
Omnibus:                        9.005   Durbin-Watson:                   1.808
Prob(Omnibus):                  0.011   Jarque-Bera (JB):                8.893
Skew:                          -0.693   Prob(JB):                       0.0117
Kurtosis:                       4.042   Cond. No.                     1.32e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.32e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

5.3.5. Regression without an interaction effect

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'continent', 'cases_neighbors']

for season in df.season.unique():
    
    results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[df_seasons.season == season]).fit()
    print(f"\n\n------------------- Season: {season} -----------------------")
    print(results.summary())

------------------- Season: winter_1 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.397
Model:                                OLS   Adj. R-squared:                  0.262
Method:                     Least Squares   F-statistic:                     2.936
Date:                    Wed, 06 Jan 2021   Prob (F-statistic):            0.00246
Time:                            11:18:18   Log-Likelihood:                -249.27
No. Observations:                      72   AIC:                             526.5
Df Residuals:                          58   BIC:                             558.4
Df Model:                              13                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                   63.2668     43.053      1.470      0.147     -22.912     149.446
continent[T.AS]             -5.0794      6.073     -0.836      0.406     -17.236       7.077
continent[T.EU]             -2.2781      4.480     -0.508      0.613     -11.247       6.691
continent[T.N.A.]            0.9213      4.764      0.193      0.847      -8.615      10.458
continent[T.OC]              1.0310      8.023      0.129      0.898     -15.028      17.090
continent[T.SA]              2.5496      5.750      0.443      0.659      -8.960      14.060
individualism_index          0.1126      0.071      1.592      0.117      -0.029       0.254
gdp_per_capita            9.285e-05   7.33e-05      1.266      0.210   -5.39e-05       0.000
population_density           0.0004      0.001      0.315      0.754      -0.002       0.003
mobility_index               0.2440      0.278      0.878      0.384      -0.312       0.800
containment_health_index     0.1483      0.156      0.952      0.345      -0.163       0.460
democracy_index              0.0052      0.095      0.055      0.956      -0.184       0.195
distance_log                -9.3564      4.501     -2.079      0.042     -18.367      -0.346
cases_neighbors              1.4852      3.945      0.376      0.708      -6.412       9.382
==============================================================================
Omnibus:                        3.147   Durbin-Watson:                   2.642
Prob(Omnibus):                  0.207   Jarque-Bera (JB):                1.819
Skew:                          -0.099   Prob(JB):                        0.403
Kurtosis:                       2.247   Cond. No.                     1.46e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.46e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: spring -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.656
Model:                                OLS   Adj. R-squared:                  0.579
Method:                     Least Squares   F-statistic:                     8.504
Date:                    Wed, 06 Jan 2021   Prob (F-statistic):           2.72e-09
Time:                            11:18:18   Log-Likelihood:                -97.796
No. Observations:                      72   AIC:                             223.6
Df Residuals:                          58   BIC:                             255.5
Df Model:                              13                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                   -6.9110      4.850     -1.425      0.160     -16.619       2.797
continent[T.AS]              1.5341      0.733      2.094      0.041       0.067       3.001
continent[T.EU]              2.1371      0.515      4.146      0.000       1.105       3.169
continent[T.N.A.]            1.2376      0.562      2.201      0.032       0.112       2.363
continent[T.OC]             -0.1224      0.975     -0.126      0.901      -2.074       1.829
continent[T.SA]              1.7354      0.682      2.546      0.014       0.371       3.100
individualism_index          0.0121      0.009      1.317      0.193      -0.006       0.030
gdp_per_capita            2.506e-05   9.08e-06      2.760      0.008    6.89e-06    4.32e-05
population_density           0.0003      0.000      1.975      0.053      -4e-06       0.001
mobility_index              -0.0205      0.014     -1.431      0.158      -0.049       0.008
containment_health_index    -0.0102      0.018     -0.554      0.582      -0.047       0.027
democracy_index             -0.0148      0.011     -1.349      0.183      -0.037       0.007
distance_log                 1.0110      0.506      1.997      0.051      -0.002       2.024
cases_neighbors              0.0024      0.004      0.628      0.532      -0.005       0.010
==============================================================================
Omnibus:                        2.083   Durbin-Watson:                   1.427
Prob(Omnibus):                  0.353   Jarque-Bera (JB):                1.648
Skew:                          -0.369   Prob(JB):                        0.439
Kurtosis:                       3.073   Cond. No.                     1.35e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.35e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: summer -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.417
Model:                                OLS   Adj. R-squared:                  0.286
Method:                     Least Squares   F-statistic:                     3.191
Date:                    Wed, 06 Jan 2021   Prob (F-statistic):            0.00117
Time:                            11:18:18   Log-Likelihood:                -176.49
No. Observations:                      72   AIC:                             381.0
Df Residuals:                          58   BIC:                             412.8
Df Model:                              13                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -24.0972     13.329     -1.808      0.076     -50.778       2.584
continent[T.AS]              4.2484      2.128      1.996      0.051      -0.011       8.508
continent[T.EU]              5.3821      1.571      3.427      0.001       2.238       8.526
continent[T.N.A.]            2.4649      1.927      1.279      0.206      -1.392       6.322
continent[T.OC]              2.8367      2.837      1.000      0.322      -2.843       8.516
continent[T.SA]              1.7484      2.770      0.631      0.530      -3.796       7.293
individualism_index         -0.0010      0.027     -0.036      0.971      -0.056       0.054
gdp_per_capita            1.506e-05   2.57e-05      0.585      0.561   -3.64e-05    6.66e-05
population_density           0.0002      0.000      0.491      0.625      -0.001       0.001
mobility_index              -0.0076      0.029     -0.264      0.792      -0.065       0.050
containment_health_index     0.1521      0.039      3.941      0.000       0.075       0.229
democracy_index             -0.0013      0.032     -0.040      0.968      -0.066       0.064
distance_log                 1.7314      1.412      1.226      0.225      -1.095       4.557
cases_neighbors              0.0024      0.006      0.427      0.671      -0.009       0.013
==============================================================================
Omnibus:                       95.371   Durbin-Watson:                   1.907
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2034.019
Skew:                          -3.865   Prob(JB):                         0.00
Kurtosis:                      27.865   Cond. No.                     1.24e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.24e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: autumn -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.549
Model:                                OLS   Adj. R-squared:                  0.447
Method:                     Least Squares   F-statistic:                     5.422
Date:                    Wed, 06 Jan 2021   Prob (F-statistic):           2.83e-06
Time:                            11:18:18   Log-Likelihood:                -172.75
No. Observations:                      72   AIC:                             373.5
Df Residuals:                          58   BIC:                             405.4
Df Model:                              13                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -31.4920     12.889     -2.443      0.018     -57.293      -5.691
continent[T.AS]              5.5655      2.081      2.674      0.010       1.399       9.732
continent[T.EU]              6.7605      1.685      4.012      0.000       3.387      10.134
continent[T.N.A.]            3.8513      1.684      2.287      0.026       0.480       7.223
continent[T.OC]              1.7736      2.648      0.670      0.506      -3.527       7.074
continent[T.SA]              3.2303      2.004      1.612      0.112      -0.781       7.241
individualism_index          0.0101      0.025      0.403      0.688      -0.040       0.060
gdp_per_capita           -1.136e-05   2.45e-05     -0.463      0.645   -6.04e-05    3.77e-05
population_density       -4.644e-05      0.000     -0.112      0.911      -0.001       0.001
mobility_index               0.0430      0.040      1.082      0.284      -0.037       0.123
containment_health_index     0.1662      0.040      4.105      0.000       0.085       0.247
democracy_index              0.0100      0.031      0.323      0.748      -0.052       0.072
distance_log                 2.5065      1.371      1.828      0.073      -0.238       5.250
cases_neighbors              0.0005      0.002      0.270      0.788      -0.003       0.004
==============================================================================
Omnibus:                       93.753   Durbin-Watson:                   1.908
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1879.921
Skew:                          -3.792   Prob(JB):                         0.00
Kurtosis:                      26.856   Cond. No.                     1.27e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.27e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


------------------- Season: winter_2 -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.493
Model:                                OLS   Adj. R-squared:                  0.380
Method:                     Least Squares   F-statistic:                     4.346
Date:                    Wed, 06 Jan 2021   Prob (F-statistic):           4.66e-05
Time:                            11:18:18   Log-Likelihood:                -175.08
No. Observations:                      72   AIC:                             378.2
Df Residuals:                          58   BIC:                             410.0
Df Model:                              13                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -28.1049     12.955     -2.169      0.034     -54.037      -2.173
continent[T.AS]              4.5537      2.186      2.083      0.042       0.178       8.929
continent[T.EU]              4.9487      1.995      2.481      0.016       0.955       8.942
continent[T.N.A.]            3.0232      1.843      1.641      0.106      -0.665       6.712
continent[T.OC]              0.9615      2.760      0.348      0.729      -4.563       6.486
continent[T.SA]              2.5182      2.090      1.205      0.233      -1.665       6.702
individualism_index          0.0107      0.026      0.416      0.679      -0.041       0.062
gdp_per_capita            -9.27e-06    2.5e-05     -0.372      0.712   -5.92e-05    4.07e-05
population_density          -0.0002      0.000     -0.446      0.657      -0.001       0.001
mobility_index               0.0358      0.045      0.798      0.428      -0.054       0.126
containment_health_index     0.1430      0.041      3.487      0.001       0.061       0.225
democracy_index              0.0044      0.032      0.137      0.892      -0.060       0.069
distance_log                 2.2735      1.361      1.670      0.100      -0.451       4.998
cases_neighbors              0.0009      0.001      0.799      0.428      -0.001       0.003
==============================================================================
Omnibus:                       94.816   Durbin-Watson:                   1.960
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1903.211
Skew:                          -3.866   Prob(JB):                         0.00
Kurtosis:                      26.971   Cond. No.                     1.24e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.24e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

import seaborn as sns

sns.heatmap(df_seasons[vars_to_use].corr(), annot=True)

<AxesSubplot:>

6. Diagnostics

import statsmodels.api as sm

6.1. Regression with total cases

6.1.1. Homoscedasticity of residuals + functional misspecification

def get_plot(results_total, df_newest, savefig = False):
    fitted_vals = results_total.predict()
    resids = results_total.resid
    y = df_newest['confirmed_log']
    
    fig, ax = plt.subplots(1,2, figsize = (12,6))
    sns.regplot(x=fitted_vals, y=y, lowess=True, ax=ax[0], line_kws={'color': 'grey'})
    ax[0].set_title('Observed vs. Predicted Values', fontsize=14)
    ax[0].set(xlabel='Predicted', ylabel='Observed')

    sns.regplot(x=fitted_vals, y=resids, lowess=True, ax=ax[1], line_kws={'color': 'grey'})
    ax[1].set_title('Residuals vs. Predicted Values', fontsize=14)
    ax[1].set(xlabel='Predicted', ylabel='Residuals')

    if savefig:
        fig.savefig('residuals_cumulative.png')

aut = df_seasons[df_seasons.season == 'autumn']

aut[season_vars['autumn'].resid < -15]

	country	season	continent	individualism_index	health_expenditure	gdp_per_capita	over65_per_capita	population_density	mobility_index	containment_health_index	democracy_index	distance_log	individualism_gov	cases_neighbors	new_cases_per_100k	new_cases_per_100k_log
310	Tanzania	autumn	AF	25.0	3.645451	985.448173	0.026205	63.579079	-11.187826	17.363541	51.6	9.136094	434.08853	10.597085	0.0	-23.025851

6.1.1.1. Checking autumn data

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'continent',  'individualism_gov', 'cases_neighbors']

season = 'autumn'    
results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[df_seasons.season == season]).fit()
print(f"\n\n------------------- Season: {season} -----------------------")
print(results.summary())

------------------- Season: autumn -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.595
Model:                                OLS   Adj. R-squared:                  0.495
Method:                     Least Squares   F-statistic:                     5.977
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           4.97e-07
Time:                            07:46:50   Log-Likelihood:                -168.86
No. Observations:                      72   AIC:                             367.7
Df Residuals:                          57   BIC:                             401.9
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -37.2632     12.524     -2.975      0.004     -62.343     -12.183
continent[T.AS]              4.6602      2.021      2.306      0.025       0.614       8.706
continent[T.EU]              5.6948      1.664      3.423      0.001       2.363       9.027
continent[T.N.A.]            3.2374      1.627      1.989      0.051      -0.022       6.496
continent[T.OC]              0.5475      2.576      0.213      0.832      -4.611       5.706
continent[T.SA]              2.4500      1.939      1.263      0.212      -1.433       6.333
individualism_index          0.2448      0.095      2.574      0.013       0.054       0.435
gdp_per_capita           -8.304e-06   2.35e-05     -0.354      0.725   -5.53e-05    3.87e-05
population_density       -4.507e-05      0.000     -0.114      0.910      -0.001       0.001
mobility_index               0.0389      0.038      1.024      0.310      -0.037       0.115
containment_health_index     0.3267      0.074      4.422      0.000       0.179       0.475
democracy_index             -0.0029      0.030     -0.096      0.924      -0.063       0.057
distance_log                 2.2470      1.314      1.710      0.093      -0.384       4.878
individualism_gov           -0.0041      0.002     -2.550      0.013      -0.007      -0.001
cases_neighbors              0.0014      0.002      0.819      0.416      -0.002       0.005
==============================================================================
Omnibus:                       79.610   Durbin-Watson:                   1.974
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1148.897
Skew:                          -3.064   Prob(JB):                    3.31e-250
Kurtosis:                      21.586   Cond. No.                     1.29e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.29e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

df_seasons[(df_seasons['new_cases_per_100k'] == 0) & (df_seasons['season'] != 'winter_1')]

	country	season	continent	individualism_index	health_expenditure	gdp_per_capita	over65_per_capita	population_density	mobility_index	containment_health_index	democracy_index	distance_log	individualism_gov	cases_neighbors	new_cases_per_100k	new_cases_per_100k_log
310	Tanzania	autumn	AF	25.0	3.645451	985.448173	0.026205	63.579079	-11.187826	17.363541	51.6	9.136094	434.088530	10.597085	0.0	-23.025851
312	Tanzania	summer	AF	25.0	3.645451	985.448173	0.026205	63.579079	-4.145647	26.077405	51.6	9.136094	651.935125	9.552368	0.0	-23.025851
314	Tanzania	winter_2	AF	25.0	3.645451	985.448173	0.026205	63.579079	-2.186495	14.700476	51.6	9.136094	367.511905	14.925671	0.0	-23.025851

df_autumn = df_seasons[df_seasons.season == 'autumn']

def plot_values(results, df):
    fitted_vals = results.predict()
    resids = results.resid
    y = df['new_cases_per_100k_log']
    
    fig, ax = plt.subplots(1,2, figsize = (12,6))
    sns.regplot(x=fitted_vals, y=y, lowess=True, ax=ax[0], line_kws={'color': 'grey'})
    ax[0].set_title('Observed vs. Predicted Values', fontsize=14)
    ax[0].set(xlabel='Predicted', ylabel='Observed')

    sns.regplot(x=fitted_vals, y=resids, lowess=True, ax=ax[1], line_kws={'color': 'grey'})
    ax[1].set_title('Residuals vs. Predicted Values', fontsize=14)
    ax[1].set(xlabel='Predicted', ylabel='Residuals')

plot_values(results, df_seasons[df_seasons.season == 'autumn'])

Running the model without Tanzania

df_autumn = df_autumn[df_autumn.country != 'Tanzania']

results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_autumn).fit()
print(f"\n\n------------------- Season: {season} -----------------------")
print(results.summary())

------------------- Season: autumn -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.793
Model:                                OLS   Adj. R-squared:                  0.741
Method:                     Least Squares   F-statistic:                     15.31
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           2.53e-14
Time:                            07:46:58   Log-Likelihood:                -96.215
No. Observations:                      71   AIC:                             222.4
Df Residuals:                          56   BIC:                             256.4
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -22.0467      4.731     -4.660      0.000     -31.524     -12.569
continent[T.AS]              3.2832      0.756      4.345      0.000       1.770       4.797
continent[T.EU]              3.4457      0.631      5.463      0.000       2.182       4.709
continent[T.N.A.]            1.0693      0.617      1.734      0.088      -0.166       2.304
continent[T.OC]             -2.2546      0.970     -2.324      0.024      -4.198      -0.311
continent[T.SA]              0.6305      0.728      0.866      0.390      -0.828       2.089
individualism_index          0.0417      0.037      1.128      0.264      -0.032       0.116
gdp_per_capita           -1.264e-05   8.74e-06     -1.447      0.153   -3.01e-05    4.86e-06
population_density       -7.432e-05      0.000     -0.504      0.616      -0.000       0.000
mobility_index              -0.0211      0.015     -1.452      0.152      -0.050       0.008
containment_health_index     0.0379      0.031      1.204      0.234      -0.025       0.101
democracy_index              0.0145      0.011      1.296      0.200      -0.008       0.037
distance_log                 2.3798      0.489      4.865      0.000       1.400       3.360
individualism_gov           -0.0004      0.001     -0.656      0.515      -0.002       0.001
cases_neighbors              0.0012      0.001      1.914      0.061   -5.57e-05       0.002
==============================================================================
Omnibus:                       14.665   Durbin-Watson:                   1.806
Prob(Omnibus):                  0.001   Jarque-Bera (JB):               18.577
Skew:                          -0.890   Prob(JB):                     9.25e-05
Kurtosis:                       4.764   Cond. No.                     1.31e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.31e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

def plot_values(results, df):
    fitted_vals = results.predict()
    resids = results.resid
    y = df['new_cases_per_100k_log']
    
    fig, ax = plt.subplots(1,2, figsize = (12,6))
    sns.regplot(x=fitted_vals, y=y, lowess=True, ax=ax[0], line_kws={'color': 'grey'})
    ax[0].set_title('Observed vs. Predicted Values', fontsize=14)
    ax[0].set(xlabel='Predicted', ylabel='Observed')

    sns.regplot(x=fitted_vals, y=resids, lowess=True, ax=ax[1], line_kws={'color': 'grey'})
    ax[1].set_title('Residuals vs. Predicted Values', fontsize=14)
    ax[1].set(xlabel='Predicted', ylabel='Residuals')

plot_values(results, df_autumn)

sm.graphics.influence_plot(results, criterion="cooks");

6.1.1.2. Checking summer data

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'continent',  'individualism_gov', 'cases_neighbors']

season = 'summer'    
results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_seasons[df_seasons.season == season]).fit()
print(f"\n\n------------------- Season: {season} -----------------------")
print(results.summary())

------------------- Season: summer -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.423
Model:                                OLS   Adj. R-squared:                  0.282
Method:                     Least Squares   F-statistic:                     2.991
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):            0.00176
Time:                            08:02:02   Log-Likelihood:                -176.08
No. Observations:                      72   AIC:                             382.2
Df Residuals:                          57   BIC:                             416.3
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -27.1022     13.886     -1.952      0.056     -54.908       0.704
continent[T.AS]              4.1260      2.140      1.928      0.059      -0.160       8.411
continent[T.EU]              5.1252      1.608      3.188      0.002       1.906       8.345
continent[T.N.A.]            2.2478      1.952      1.152      0.254      -1.660       6.156
continent[T.OC]              2.4160      2.894      0.835      0.407      -3.379       8.211
continent[T.SA]              1.6003      2.785      0.575      0.568      -3.976       7.176
individualism_index          0.0784      0.103      0.763      0.449      -0.127       0.284
gdp_per_capita            1.223e-05    2.6e-05      0.469      0.641   -3.99e-05    6.44e-05
population_density           0.0002      0.000      0.539      0.592      -0.001       0.001
mobility_index              -0.0060      0.029     -0.206      0.837      -0.064       0.052
containment_health_index     0.2036      0.075      2.713      0.009       0.053       0.354
democracy_index             -0.0033      0.033     -0.102      0.919      -0.069       0.062
distance_log                 1.7596      1.417      1.242      0.219      -1.077       4.596
individualism_gov           -0.0013      0.002     -0.802      0.426      -0.005       0.002
cases_neighbors              0.0019      0.006      0.346      0.731      -0.009       0.013
==============================================================================
Omnibus:                       91.401   Durbin-Watson:                   1.897
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1778.080
Skew:                          -3.649   Prob(JB):                         0.00
Kurtosis:                      26.226   Cond. No.                     1.29e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.29e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

df_summer = df_seasons[df_seasons.season == 'summer']

def plot_values(results, df):
    fitted_vals = results.predict()
    resids = results.resid
    y = df['new_cases_per_100k_log']
    
    fig, ax = plt.subplots(1,2, figsize = (12,6))
    sns.regplot(x=fitted_vals, y=y, lowess=True, ax=ax[0], line_kws={'color': 'grey'})
    ax[0].set_title('Observed vs. Predicted Values', fontsize=14)
    ax[0].set(xlabel='Predicted', ylabel='Observed')

    sns.regplot(x=fitted_vals, y=resids, lowess=True, ax=ax[1], line_kws={'color': 'grey'})
    ax[1].set_title('Residuals vs. Predicted Values', fontsize=14)
    ax[1].set(xlabel='Predicted', ylabel='Residuals')

plot_values(results, df_seasons[df_seasons.season == 'summer'])

Running the model without Tanzania

df_summer = df_summer[df_summer.country != 'Tanzania']

results = smf.ols('new_cases_per_100k_log ~ ' + ' + '.join(vars_to_use), data = df_summer).fit()
print(f"\n\n------------------- Season: {season} -----------------------")
print(results.summary())

------------------- Season: summer -----------------------
                              OLS Regression Results                              
==================================================================================
Dep. Variable:     new_cases_per_100k_log   R-squared:                       0.523
Model:                                OLS   Adj. R-squared:                  0.404
Method:                     Least Squares   F-statistic:                     4.388
Date:                    Thu, 07 Jan 2021   Prob (F-statistic):           3.33e-05
Time:                            08:02:14   Log-Likelihood:                -112.70
No. Observations:                      71   AIC:                             255.4
Df Residuals:                          56   BIC:                             289.3
Df Model:                              14                                         
Covariance Type:                nonrobust                                         
============================================================================================
                               coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------
Intercept                  -12.4994      5.966     -2.095      0.041     -24.451      -0.548
continent[T.AS]              1.5181      0.923      1.644      0.106      -0.331       3.367
continent[T.EU]              2.1529      0.707      3.044      0.004       0.736       3.570
continent[T.N.A.]            0.7208      0.834      0.864      0.391      -0.950       2.392
continent[T.OC]             -0.4823      1.242     -0.388      0.699      -2.971       2.006
continent[T.SA]              0.5209      1.184      0.440      0.662      -1.852       2.894
individualism_index         -0.0478      0.044     -1.079      0.285      -0.137       0.041
gdp_per_capita            1.235e-05   1.11e-05      1.117      0.269   -9.81e-06    3.45e-05
population_density           0.0002      0.000      1.041      0.302      -0.000       0.001
mobility_index              -0.0193      0.012     -1.568      0.122      -0.044       0.005
containment_health_index     0.0185      0.034      0.547      0.587      -0.049       0.086
democracy_index             -0.0050      0.014     -0.362      0.719      -0.033       0.023
distance_log                 1.6458      0.602      2.736      0.008       0.441       2.851
individualism_gov            0.0008      0.001      1.119      0.268      -0.001       0.002
cases_neighbors              0.0009      0.002      0.368      0.714      -0.004       0.006
==============================================================================
Omnibus:                        5.196   Durbin-Watson:                   2.134
Prob(Omnibus):                  0.074   Jarque-Bera (JB):                4.555
Skew:                          -0.609   Prob(JB):                        0.103
Kurtosis:                       3.235   Cond. No.                     1.31e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.31e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

plot_values(results, df_summer)

sm.graphics.influence_plot(results, criterion="cooks");

6.1.1.3. Diagnostics for all seasons

season_vars = get_season_vars(with_tanzania=False)

season_vars['cumulative'] = results_total2
keys_list = list(season_vars.keys())
keys_list.insert(0, keys_list.pop())
season_vars = dict(sorted(season_vars.items(), key = lambda pair: keys_list.index(pair[0])))

df_seasons2 = df_seasons[df_seasons.index != 'Tanzania'].copy()

season_vars.keys()

dict_keys(['cumulative', 'winter_1', 'spring', 'summer', 'autumn', 'winter_2'])

item_plots = {'cumulative': [0,1],
              'winter_1': [2,3],
              'spring': [4,5],
              'summer': [6,7],
              'autumn': [8,9],
              'winter_2': [10,11]}

fig, axs = plt.subplots(3,4, figsize = (18,12))

ax_list = [item for sublist in axs for item in sublist]

for season, model in season_vars.items():

    fitted_vals = model.predict()
    resids = model.resid
    if season == 'cumulative': y = df_newest['confirmed_log']
    else: y = df_seasons2.loc[(df_seasons2.season == season, 'new_cases_per_100k_log') ]

    # get items
    plots = item_plots[season]
    
    for plot in plots:
        ax = ax_list.pop(0)
        
        if plot % 2 == 0:
            sns.regplot(x=fitted_vals, y=y, lowess=True, ax=ax, line_kws={'color': 'grey'})
            ax.set_title(f'Model: {season}\n Observed vs. Predicted Values', fontsize=14)
            ax.set(xlabel='Predicted', ylabel='Observed')
        else:
            sns.regplot(x=fitted_vals, y=resids, lowess=True, ax=ax, line_kws={'color': 'grey'})
            ax.set_title(f'Model: {season}\n Residuals vs. Predicted Values', fontsize=14)
            ax.set(xlabel='Predicted', ylabel='Residuals')
            
plt.tight_layout()
fig.savefig('resids.png')

season_vars

{'cumulative': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x1d3213c61f0>,
 'winter_1': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x1d32243d8b0>,
 'spring': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x1d3249ba7f0>,
 'summer': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x1d3249c9fa0>,
 'autumn': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x1d3249db340>,
 'winter_2': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x1d3249e9220>}

get_plot(results_total, df_newest, savefig=True)

6.1.2. Multicolinearity

from functools import reduce

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 'individualism_gov',
              'cases_neighbors']

vif = pd.DataFrame()
vif['VIF'] = [variance_inflation_factor(df[vars_to_use].values, i) for i in range(df[vars_to_use].shape[1])]
vif['variable'] = df[vars_to_use].columns

season_vars

{'cumulative': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2299a6c4370>,
 'winter_1': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2299c1ade80>,
 'spring': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2299c2a6c70>,
 'summer': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2299c5532b0>,
 'autumn': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2299c56ff40>,
 'winter_2': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2299c566f40>}

6.1.2.1.Overall model

df2 = df.copy()
df2 = pd.concat((df2.drop('continent', axis=1), pd.get_dummies(df2['continent'])), axis=1)

df2 = df2.rename(columns={'N.A.': 'NA'})

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 
              'cases_neighbors', 'AF', 'AS', 'EU', 'NA', 'OC']

def join_strings(xs, sep):
    return reduce(lambda a, b: a + sep + b, xs)
    
vifs = {}

for v in vars_to_use:
    cns = vars_to_use.copy()
    cns.remove(v)
    formula = v + " ~ " + join_strings(cns, " + ")
    coef_det = smf.ols(formula, data = df2).fit()
    vif = 1 / (1 - coef_det.rsquared)
    vifs[v] = vif
    if vif > 3:
        print("\n" + 80 * "=")
        print(v)
        print(vif)
        
multicolinearity_df = pd.DataFrame(vifs.items())

================================================================================
distance_log
4.529382769257378

================================================================================
AS
9.840883109482503

================================================================================
EU
6.892263022892055

with open('corr_coef.tex','w') as tf:
    tf.write(df2[vars_to_use].corr().to_latex())

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 
              'cases_neighbors']

df_corr = df2[vars_to_use].corr()

df2_c = df2[vars_to_use]
df2_c.columns = ['ind', 'gdp' ,'popdens', 'mob', 'health', 'democr', 'dist', 'neighb']

df2_c.corr()

with open('corr_coef.tex','w') as tf:
    tf.write(df2_c.corr().to_latex())

multicolinearity_df.columns = ['Variable', 'VIF']

with open('multicolinearity.tex','w') as tf:
    tf.write(multicolinearity_df.to_latex())

6.1.3. Homoscedasticity of residuals

import statsmodels.stats.api as sms

stder = {}
for season, fit in season_vars.items():
    stder[season] = {}


names = ['Lagrange multiplier statistic', 'p-value',
        'F-statistic', 'p-value for F-statistic']
for season, fit in season_vars.items():
    test = sms.het_breuschpagan(fit.resid, fit.model.exog)
    items = {*(zip(names,test))}
    for it in items:
        stder[season][it[0]] = it[1]
    

stder = pd.DataFrame(stder).round(4)

with open('breuschp.tex','w') as tf:
    tf.write(stder.to_latex())

OLSResults.et_robustcov_results()

6.1.4. Autocorrelation of residuals

import statsmodels.tsa.api as smt

acf = smt.graphics.plot_acf(results_total.resid, lags=40 , alpha=0.05)
acf.show()

<ipython-input-86-5396dca5761b>:2: UserWarning: Matplotlib is currently using module://ipykernel.pylab.backend_inline, which is a non-GUI backend, so cannot show the figure.
  acf.show()

season_vars

{'cumulative': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2299a6c4370>,
 'winter_1': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2299c1ade80>,
 'spring': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2299c2a6c70>,
 'summer': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2299c5532b0>,
 'autumn': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2299c56ff40>,
 'winter_2': <statsmodels.regression.linear_model.RegressionResultsWrapper at 0x2299c566f40>}

fig, axs = plt.subplots(2,3, figsize = (18,8))
ax_list = [item for sublist in axs for item in sublist]

for season, model in season_vars.items():
    ax = ax_list.pop(0)
    acf = smt.graphics.plot_acf(model.resid, lags=10 , alpha=0.05, ax=ax)
    ax.set_title(f"Model: {season}", fontsize = 16)
    
    
plt.tight_layout()
fig.savefig('autocorrelation.png')

There is no autocorrelation is the residuals

# Durbin Watson test
from statsmodels.stats.stattools import durbin_watson

durbs = {}
for season, model in season_vars.items():
    durbs[season] = durbin_watson(model.resid)

durbs_df = pd.DataFrame(durbs.items())
durbs_df.columns=['Model', 'Durbin-Watson statistic']

with open('dw_test.tex','w') as tf:
    tf.write(durbs_df.to_latex())

durbin_watson(results_total.resid)

1.6113160773978314

durbin_watson(results.resid)

2.1343740259697963

According to the sample size and number of regressors, the statistics should be in the range of 1.369 and 1.910 as presented by the DW statistical table. This means that the model is not suffering from serial correlation in the residuals.

6.1.5. Features and residuals are uncorrelated

df_newest

	country	month	idv	confirmed	dead	population	current_health_expenditure_of_gdp	gdp_per_capita_constant_2010_us	population_ages_65_and_above_total	population_density_people_per_sq_km_of_land_area	...	containment_health_index	democracy_index	capital	distance	continent	confirmed_log	current_health_expenditure_of_gdp_log	distance_log	gdp_per_capita_constant_2010_us_log	season
10	Argentina	12.0	46.0	1602163.0	43018.0	44938712.0	9.124315	9729.141574	5052508.0	16.258510	...	73.400000	70.2	Buenos Aires	19206.559549	SA	14.286865	2.210943	9.863007	9.182881	winter_2
21	Australia	12.0	90.0	28381.0	909.0	25364307.0	9.205948	57071.168295	4038302.0	3.247871	...	60.961935	90.9	Canberra	8153.589761	OC	10.253475	2.219850	9.006214	10.952054	winter_2
32	Austria	12.0	55.0	356351.0	6086.0	8877067.0	10.396617	50654.730148	1693354.0	107.127967	...	72.941579	82.9	Vienna	8081.565310	EU	12.783671	2.341480	8.997341	10.832788	winter_2
43	Bangladesh	12.0	20.0	512496.0	7531.0	163046161.0	2.274249	1287.821425	8446364.0	1239.579312	...	72.120000	58.8	Dhaka	2477.356735	AS	13.147048	0.821650	7.814947	7.160707	winter_2
54	Belarus	12.0	25.0	192361.0	1414.0	9466856.0	5.925786	6678.509065	1439042.0	46.719504	...	36.265714	24.8	Minsk	7119.018739	EU	12.167129	1.779313	8.870525	8.806650	winter_2
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
747	United Kingdom	12.0	89.0	2432892.0	72548.0	66834405.0	9.631694	43688.437455	12370177.0	274.708982	...	66.425556	85.2	London	8894.845144	EU	14.704591	2.265059	9.093227	10.684839	winter_2
758	United States	12.0	91.0	19346790.0	335789.0	328239523.0	17.061269	55809.007792	53206334.0	35.713622	...	63.078571	79.6	Washington D.C.	12222.325032	N.A.	16.778037	2.836811	9.411019	10.929691	winter_2
769	Uruguay	12.0	36.0	17962.0	168.0	3461734.0	9.296212	14597.308096	517226.0	19.708028	...	53.426552	83.8	Montevideo	19011.570501	SA	9.796014	2.229607	9.852803	9.588592	winter_2
780	Vietnam	12.0	20.0	1456.0	35.0	96462106.0	5.532128	2082.243694	7286432.0	308.125246	...	56.821429	30.8	Hanoi	1355.430475	AS	7.283448	1.710573	7.211874	7.641201	winter_2
791	Zambia	12.0	35.0	20462.0	386.0	17861030.0	4.470341	1658.135434	377817.0	23.341479	...	53.677391	50.9	Lusaka	10501.353873	AF	9.926325	1.497465	9.259259	7.413449	winter_2

72 rows × 29 columns

from scipy.stats.stats import pearsonr
corr_error = {}
for column in vars_to_use:
    if not isinstance(df_newest[column].iloc[0], str):
        corr_test = pearsonr(df_newest[column], results_total.resid)
        corr_error[column] = {'correlation': corr_test[0].round(4), 'p-value': corr_test[1].round(4)}
        print(f'Variable: {column} --- correlation: {corr_test[0]:.4f}, p-value: {corr_test[1]:.4f}')

Variable: individualism_index --- correlation: -0.0000, p-value: 1.0000
Variable: gdp_per_capita --- correlation: -0.0000, p-value: 1.0000
Variable: population_density --- correlation: -0.0000, p-value: 1.0000
Variable: mobility_index --- correlation: 0.0115, p-value: 0.9235
Variable: containment_health_index --- correlation: 0.0567, p-value: 0.6363
Variable: democracy_index --- correlation: -0.0000, p-value: 1.0000
Variable: distance_log --- correlation: -0.0000, p-value: 1.0000
Variable: cases_neighbors --- correlation: 0.0000, p-value: 1.0000

vars_to_use = ['individualism_index', 'gdp_per_capita', 
               'population_density', 
               'mobility_index', 'containment_health_index', 'democracy_index', 'distance_log', 
              'cases_neighbors']

corr_error = {}

for season, model in season_vars.items():
    corr_error[season] = {}
    
for season, model in season_vars.items():
    for column in vars_to_use:
        if season == 'cumulative': df_ = df_newest2[vars_to_use].copy()
        else: df_ = df_seasons2.loc[df_seasons2.season == season, vars_to_use].copy()
        if not isinstance(df_[column].iloc[0], str):
            corr_test = pearsonr(df_[column], model.resid)
            corr_error[season][column] = corr_test[0].round(4)

corr_error = pd.DataFrame(corr_error)

with open('corr_error.tex','w') as tf:
    tf.write(corr_error.to_latex())

There is no relationship between any of the predictors and the error term.

6.1.6. Outliers

fitted_vals = results_total.predict()
resids = results_total.resid
y = df_newest['confirmed_log']

df_newest[df_newest.index == 780]

	country	month	idv	confirmed	dead	population	current_health_expenditure_of_gdp	gdp_per_capita_constant_2010_us	population_ages_65_and_above_total	population_density_people_per_sq_km_of_land_area	...	containment_health_index	democracy_index	capital	distance	continent	confirmed_log	current_health_expenditure_of_gdp_log	distance_log	gdp_per_capita_constant_2010_us_log	season
780	Vietnam	12.0	20.0	1456.0	35.0	96462106.0	5.532128	2082.243694	7286432.0	308.125246	...	56.821429	30.8	Hanoi	1355.430475	AS	7.283448	1.710573	7.211874	7.641201	winter_2

1 rows × 29 columns

results_total2 = smf.ols('confirmed_log ~ ' + ' + '.join(vars_to_use), data = df_newest[df_newest.country != 'Vietnam']).fit()

results_total2.summary()

OLS Regression Results

Dep. Variable:	confirmed_log	R-squared:	0.474
Model:	OLS	Adj. R-squared:	0.397
Method:	Least Squares	F-statistic:	6.119
Date:	Sun, 03 Jan 2021	Prob (F-statistic):	4.34e-06
Time:	14:17:02	Log-Likelihood:	-125.63
No. Observations:	71	AIC:	271.3
Df Residuals:	61	BIC:	293.9
Df Model:	9
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Intercept	9.7351	3.794	2.566	0.013	2.149	17.322
idv	0.0194	0.012	1.578	0.120	-0.005	0.044
current_health_expenditure_of_gdp	0.3192	0.111	2.869	0.006	0.097	0.542
gdp_per_capita_constant_2010_us	-1.751e-05	1.23e-05	-1.424	0.160	-4.21e-05	7.09e-06
over65_per_capita	-2.4652	4.478	-0.550	0.584	-11.420	6.490
population_density_people_per_sq_km_of_land_area	-6.924e-05	0.000	-0.324	0.747	-0.000	0.000
mobility_index	0.0020	0.022	0.092	0.927	-0.042	0.046
containment_health_index	0.1059	0.020	5.413	0.000	0.067	0.145
democracy_index	-0.0412	0.015	-2.668	0.010	-0.072	-0.010
distance_log	-0.3605	0.410	-0.879	0.383	-1.180	0.459

Omnibus:	1.090	Durbin-Watson:	1.681
Prob(Omnibus):	0.580	Jarque-Bera (JB):	0.795
Skew:	-0.259	Prob(JB):	0.672
Kurtosis:	3.028	Cond. No.	9.20e+05

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 9.2e+05. This might indicate that there are
strong multicollinearity or other numerical problems.

results_total.summary()

OLS Regression Results

Dep. Variable:	confirmed_log	R-squared:	0.409
Model:	OLS	Adj. R-squared:	0.323
Method:	Least Squares	F-statistic:	4.767
Date:	Sun, 03 Jan 2021	Prob (F-statistic):	7.78e-05
Time:	14:18:00	Log-Likelihood:	-134.24
No. Observations:	72	AIC:	288.5
Df Residuals:	62	BIC:	311.3
Df Model:	9
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Intercept	3.8786	3.791	1.023	0.310	-3.699	11.456
idv	0.0200	0.013	1.484	0.143	-0.007	0.047
current_health_expenditure_of_gdp	0.2310	0.119	1.935	0.058	-0.008	0.470
gdp_per_capita_constant_2010_us	-1.678e-05	1.35e-05	-1.242	0.219	-4.38e-05	1.02e-05
over65_per_capita	-0.4140	4.882	-0.085	0.933	-10.173	9.345
population_density_people_per_sq_km_of_land_area	-1.116e-05	0.000	-0.048	0.962	-0.000	0.000
mobility_index	0.0078	0.024	0.325	0.747	-0.040	0.056
containment_health_index	0.1071	0.021	4.986	0.000	0.064	0.150
democracy_index	-0.0316	0.017	-1.887	0.064	-0.065	0.002
distance_log	0.2459	0.413	0.595	0.554	-0.580	1.072

Omnibus:	6.645	Durbin-Watson:	1.531
Prob(Omnibus):	0.036	Jarque-Bera (JB):	5.971
Skew:	-0.578	Prob(JB):	0.0505
Kurtosis:	3.810	Cond. No.	8.89e+05

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 8.89e+05. This might indicate that there are
strong multicollinearity or other numerical problems.

get_plot(results_total2, df_newest[df_newest.country != 'Vietnam'])

Results do not change after checking for outliers

6.1.7. High leverage points

fig, axs = plt.subplots(3,2, figsize = (15,12))
ax_list = [item for sublist in axs for item in sublist]

for season, model in season_vars.items():
    ax = ax_list.pop(0)
    sm.graphics.influence_plot(model, criterion = 'cooks', ax=ax, size = 0.1, alpha = 0.001)
    ax.set_title(f"Model: {season}", fontsize = 16)
    
    
plt.tight_layout()
fig.savefig('leverage.png')

results_total3 = smf.ols('confirmed_log ~ ' + ' + '.join(vars_to_use), data = df_newest[df_newest.country != 'Singapore']).fit()

get_plot(results_total3, df_newest[df_newest.country != 'Singapore'])

results_total3.summary()

OLS Regression Results

Dep. Variable:	confirmed_log	R-squared:	0.425
Model:	OLS	Adj. R-squared:	0.340
Method:	Least Squares	F-statistic:	5.009
Date:	Sun, 03 Jan 2021	Prob (F-statistic):	4.72e-05
Time:	14:26:54	Log-Likelihood:	-131.72
No. Observations:	71	AIC:	283.4
Df Residuals:	61	BIC:	306.1
Df Model:	9
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Intercept	4.9336	3.832	1.287	0.203	-2.730	12.597
idv	0.0196	0.013	1.466	0.148	-0.007	0.046
current_health_expenditure_of_gdp	0.2373	0.118	2.002	0.050	0.000	0.474
gdp_per_capita_constant_2010_us	-1.985e-05	1.36e-05	-1.463	0.149	-4.7e-05	7.29e-06
over65_per_capita	-0.2135	4.844	-0.044	0.965	-9.900	9.473
population_density_people_per_sq_km_of_land_area	-0.0013	0.001	-1.391	0.169	-0.003	0.001
mobility_index	0.0169	0.025	0.688	0.494	-0.032	0.066
containment_health_index	0.1160	0.022	5.224	0.000	0.072	0.160
democracy_index	-0.0278	0.017	-1.656	0.103	-0.061	0.006
distance_log	0.0842	0.425	0.198	0.844	-0.766	0.934

Omnibus:	5.912	Durbin-Watson:	1.469
Prob(Omnibus):	0.052	Jarque-Bera (JB):	5.131
Skew:	-0.542	Prob(JB):	0.0769
Kurtosis:	3.746	Cond. No.	8.71e+05

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 8.71e+05. This might indicate that there are
strong multicollinearity or other numerical problems.

Singapore, the point with high leverage, does not change any of the conclusions reached

6.1.8. Normality of residuals

from scipy import stats

def normality_of_residuals_test(model):
    '''
    Function for drawing the normal QQ-plot of the residuals and running 4 statistical tests to 
    investigate the normality of residuals.
    
    Arg:
    * model - fitted OLS models from statsmodels
    '''
    sm.ProbPlot(model.resid).qqplot(line='s');
    plt.title('Q-Q plot');

    jb = stats.jarque_bera(model.resid)
    sw = stats.shapiro(model.resid)
    ad = stats.anderson(model.resid, dist='norm')
    ks = stats.kstest(model.resid, 'norm')
    
    print(f'Jarque-Bera test ---- statistic: {jb[0]:.4f}, p-value: {jb[1]}')
    print(f'Shapiro-Wilk test ---- statistic: {sw[0]:.4f}, p-value: {sw[1]:.4f}')
    print(f'Kolmogorov-Smirnov test ---- statistic: {ks.statistic:.4f}, p-value: {ks.pvalue:.4f}')
    print(f'Anderson-Darling test ---- statistic: {ad.statistic:.4f}, 5% critical value: {ad.critical_values[2]:.4f}')
    print('If the returned AD statistic is larger than the critical value, then for the 5% significance level, the null hypothesis that the data come from the Normal distribution should be rejected. ')

fig, axs = plt.subplots(3,2, figsize = (15,12))
ax_list = [item for sublist in axs for item in sublist]

for season, model in season_vars.items():
    ax = ax_list.pop(0)
    sm.ProbPlot(model.resid).qqplot(line='s', ax=ax);
    ax.set_title(f"Model: {season}", fontsize = 16)
    
    
plt.tight_layout()
fig.savefig('normality_tests.png')

fig, axs = plt.subplots(3,2, figsize = (15,12))
ax_list = [item for sublist in axs for item in sublist]

for season, model in season_vars.items():
    ax = ax_list.pop(0)
    sm.ProbPlot(model.resid).qqplot(line='s', ax=ax);
    ax.set_title(f"Model: {season}", fontsize = 16)
    
    
plt.tight_layout()
fig.savefig('normality_tests.png')

tests = {}
for season, model in season_vars.items():

    jb = stats.jarque_bera(model.resid)
    sw = stats.shapiro(model.resid)
    ad = stats.anderson(model.resid, dist='norm')
    ks = stats.kstest(model.resid, 'norm')
    tests[season] = {'Jarque-Bera test': jb[1],
                     'Shapiro-Wilk test': sw[1],
                     'Kolmogorov-Smirnov test': ks.pvalue}

tests = pd.DataFrame(tests).round(4)

with open('tests_norm.tex','w') as tf:
    tf.write(tests.to_latex())

normality_of_residuals_test(results_total)

Jarque-Bera test ---- statistic: 22.2804, p-value: 1.4517044101491905e-05
Shapiro-Wilk test ---- statistic: 0.9489, p-value: 0.0055
Kolmogorov-Smirnov test ---- statistic: 0.1108, p-value: 0.3161
Anderson-Darling test ---- statistic: 0.8127, 5% critical value: 0.7490
If the returned AD statistic is larger than the critical value, then for the 5% significance level, the null hypothesis that the data come from the Normal distribution should be rejected. 

7. Additional checks

7.1. Sensitivity check

def y_model(ind, cont):
    return 10 + 0.048 * ind + 0.211 * cont - 0.001* (ind*cont)

y_model(10, 30)

16.51

for cont in [20,50,80]:
    print()
    print()
    print(f"------- CONT: {cont}----------------------")
    for ind in range(5,100,5):
        print(f"Individualism: {ind}, Results: {y_model(ind, cont)}")

------- CONT: 20----------------------
Individualism: 5, Results: 14.360000000000001
Individualism: 10, Results: 14.5
Individualism: 15, Results: 14.64
Individualism: 20, Results: 14.78
Individualism: 25, Results: 14.919999999999998
Individualism: 30, Results: 15.06
Individualism: 35, Results: 15.2
Individualism: 40, Results: 15.34
Individualism: 45, Results: 15.479999999999999
Individualism: 50, Results: 15.620000000000001
Individualism: 55, Results: 15.76
Individualism: 60, Results: 15.899999999999999
Individualism: 65, Results: 16.04
Individualism: 70, Results: 16.18
Individualism: 75, Results: 16.32
Individualism: 80, Results: 16.459999999999997
Individualism: 85, Results: 16.6
Individualism: 90, Results: 16.74
Individualism: 95, Results: 16.880000000000003


------- CONT: 50----------------------
Individualism: 5, Results: 20.54
Individualism: 10, Results: 20.53
Individualism: 15, Results: 20.52
Individualism: 20, Results: 20.509999999999998
Individualism: 25, Results: 20.5
Individualism: 30, Results: 20.49
Individualism: 35, Results: 20.479999999999997
Individualism: 40, Results: 20.47
Individualism: 45, Results: 20.46
Individualism: 50, Results: 20.45
Individualism: 55, Results: 20.439999999999998
Individualism: 60, Results: 20.43
Individualism: 65, Results: 20.42
Individualism: 70, Results: 20.409999999999997
Individualism: 75, Results: 20.4
Individualism: 80, Results: 20.39
Individualism: 85, Results: 20.38
Individualism: 90, Results: 20.369999999999997
Individualism: 95, Results: 20.36


------- CONT: 80----------------------
Individualism: 5, Results: 26.72
Individualism: 10, Results: 26.56
Individualism: 15, Results: 26.400000000000002
Individualism: 20, Results: 26.24
Individualism: 25, Results: 26.08
Individualism: 30, Results: 25.92
Individualism: 35, Results: 25.759999999999998
Individualism: 40, Results: 25.599999999999998
Individualism: 45, Results: 25.439999999999998
Individualism: 50, Results: 25.28
Individualism: 55, Results: 25.119999999999997
Individualism: 60, Results: 24.959999999999997
Individualism: 65, Results: 24.8
Individualism: 70, Results: 24.639999999999997
Individualism: 75, Results: 24.479999999999997
Individualism: 80, Results: 24.32
Individualism: 85, Results: 24.16
Individualism: 90, Results: 24.0
Individualism: 95, Results: 23.839999999999996

7.2. Check on average government intervention

df = pd.read_csv('2021-01-04 final_data.csv')
df = df[df.country != 'Tanzania']

fig, axs = plt.subplots(3,4, figsize = (20,15))

ax_list = [item for sublist in axs for item in sublist]
for month in range(2,13):
    ax = ax_list.pop(0)
    
    df_ = df[df.month == month]
    sns.regplot(x = 'individualism_index', y = 'containment_health_index', data = df_, ax=ax)
    ax.set_title(f"Month: {month}")

fig, axs = plt.subplots(3,4, figsize = (20,15))

ax_list = [item for sublist in axs for item in sublist]
for month in range(2,13):
    ax = ax_list.pop(0)
    
    df_ = df[df.month == month]
    sns.regplot(x = 'individualism_index', y = 'containment_health_index', data = df_, ax=ax, order = 2)
    ax.set_title(f"Month: {month}")

fig, axs = plt.subplots(3,4, figsize = (20,15))

ax_list = [item for sublist in axs for item in sublist]
for month in range(2,13):
    ax = ax_list.pop(0)
    
    df_ = df[df.month == month]
    sns.scatterplot(x = 'individualism_index', y = 'containment_health_index',
                    hue = 'new_cases_per_100k_log',
                    size ='new_cases_per_100k_log',
                    data = df_, ax=ax)
    ax.set_title(f"Month: {month}")

df_newest = df[df.month==12]

df_newest = df_newest.set_index('country')

df_newest['mobility_index_avg'] = df.groupby('country').mobility_index.mean()
df_newest['containment_health_index_avg'] = df.groupby('country').containment_health_index.mean()

df_newest = get_interactions(df_newest, month_12=True)

df_newest['confirmed_per_100k'] = (df_newest['confirmed'] / df_newest['population'] ) * 100_000
df_newest['confirmed_per_100k_log'] = np.log(df_newest['confirmed_per_100k'])

fig, ax = plt.subplots(figsize=(12,7))

sns.scatterplot(x = 'individualism_index', y = 'containment_health_index_avg',
                hue = 'confirmed_per_100k_log',
                size ='confirmed_per_100k_log',
                data = df_newest, ax=ax);

fig, axs = plt.subplots(3,4, figsize = (20,15))

ax_list = [item for sublist in axs for item in sublist]
for month in range(2,13):
    ax = ax_list.pop(0)
    
    df_ = df[df.month == month]
    sns.scatterplot(x = 'new_cases_per_100k_log', y = 'containment_health_index',
                    size ='individualism_index',
                    data = df_, ax=ax)
    ax.set_title(f"Month: {month}")

sns.regplot(x = 'individualism_index', y = 'containment_health_index_avg', data = df_newest, order = 2)

<AxesSubplot:xlabel='individualism_index', ylabel='containment_health_index_avg'>

7.3. MCAR test

import scipy.stats as st

def checks_input_mcar_tests(data):
    """ Checks whether the input parameter of class McarTests is correct
            Parameters
            ----------
            data:
                The input of McarTests specified as 'data'
            Returns
            -------
            bool
                True if input is correct
            """

    if not isinstance(data, pd.DataFrame):
        print("Error: Data should be a Pandas DataFrame")
        return False

    if not any(data.dtypes.values == np.float):
        if not any(data.dtypes.values == np.int):
            print("Error: Dataset cannot contain other value types than floats and/or integers")
            return False

    if not data.isnull().values.any():
        print("Error: No NaN's in given data")
        return False

    return True

class McarTests():

    def __init__(self, data):
        self.data = data

    def mcar_test(self):
        """ Implementation of Little's MCAR test
        Parameters
        ----------
        data: Pandas DataFrame
            An incomplete dataset with samples as index and variables as columns
        Returns
        -------
        p_value: Float
            This value is the outcome of a chi-square statistical test, testing whether the null hypothesis
            'the missingness mechanism of the incomplete dataset is MCAR' can be rejected.
        """

        if not checks_input_mcar_tests(self.data):
            raise Exception("Input not correct")

        dataset = self.data.copy()
        vars = dataset.dtypes.index.values
        n_var = dataset.shape[1]

        # mean and covariance estimates
        # ideally, this is done with a maximum likelihood estimator
        gmean = dataset.mean()
        gcov = dataset.cov()

        # set up missing data patterns
        r = 1 * dataset.isnull()
        mdp = np.dot(r, list(map(lambda x: ma.pow(2, x), range(n_var))))
        sorted_mdp = sorted(np.unique(mdp))
        n_pat = len(sorted_mdp)
        correct_mdp = list(map(lambda x: sorted_mdp.index(x), mdp))
        dataset['mdp'] = pd.Series(correct_mdp, index=dataset.index)

        # calculate statistic and df
        pj = 0
        d2 = 0
        for i in range(n_pat):
            dataset_temp = dataset.loc[dataset['mdp'] == i, vars]
            select_vars = ~dataset_temp.isnull().any()
            pj += np.sum(select_vars)
            select_vars = vars[select_vars]
            means = dataset_temp[select_vars].mean() - gmean[select_vars]
            select_cov = gcov.loc[select_vars, select_vars]
            mj = len(dataset_temp)
            parta = np.dot(means.T, np.linalg.solve(select_cov, np.identity(select_cov.shape[1])))
            d2 += mj * (np.dot(parta, means))

        df = pj - n_var

        # perform test and save output
        p_value = 1 - st.chi2.cdf(d2, df)

        return p_value

    def mcar_t_tests(self):
        """ MCAR tests for each pair of variables
        Parameters
        ----------
        data: Pandas DataFrame
            An incomplete dataset with samples as index and variables as columns
        Returns
        -------
        mcar_matrix: Pandas DataFrame
            A square Pandas DataFrame containing True/False for each pair of variables
            True: Missingness in index variable is MCAR for column variable
            False: Missingness in index variable is not MCAR for column variable
        """

        if not checks_input_mcar_tests(self.data):
            raise Exception("Input not correct")

        dataset = self.data.copy()
        vars = dataset.dtypes.index.values
        mcar_matrix = pd.DataFrame(data=np.zeros(shape=(dataset.shape[1], dataset.shape[1])),
                                   columns=vars, index=vars)

        for var in vars:
            for tvar in vars:
                part_one = dataset.loc[dataset[var].isnull(), tvar].dropna()
                part_two = dataset.loc[~dataset[var].isnull(), tvar].dropna()
                mcar_matrix.loc[var, tvar] = st.ttest_ind(part_one, part_two, equal_var=False).pvalue

        mcar_matrix = mcar_matrix[mcar_matrix.notnull()] > 0.05

        return mcar_matrix

checks_input_mcar_tests(df)

Error: No NaN's in given data

False

7.4. GDP calculations

df['gdp'] = df['gdp_per_capita'] * df['population']

with open('corr_coef_gdp.tex','w') as tf:
    tf.write(df[df.month == 12][['gdp', 'gdp_per_capita', 'individualism_index']].corr().to_latex())

fig, axs = plt.subplots(3,4, figsize = (20,15))

ax_list = [item for sublist in axs for item in sublist]
for month in range(2,13):
    ax = ax_list.pop(0)
    
    df_ = df[df.month == month]
    sns.regplot(x = 'democracy_index', y = 'containment_health_index', data = df_, ax=ax)
    ax.set_title(f"Month: {month}")

df4 = df.groupby(['country']).agg({'containment_health_index': ['std'], 
                             'democracy_index': 'mean'})

sns.regplot(x = 'democracy_index', y = 'containment_health_index', data = df4)

<AxesSubplot:xlabel='mean', ylabel='std'>

7.5. Stringency

df['individualism_index'].mean()

42.309859154929576

plt.hist(df['individualism_index']);

df['ind_category'] = df['individualism_index'].map(lambda x: 'high' if x >= 60 else 'low' if x <= 25 else 'medium')

df['ind_category'].value_counts() / 11

medium    27.0
low       22.0
high      22.0
Name: ind_category, dtype: float64

dfn = df[df.month == 12].copy()

fig, axs = plt.subplots(10,2,figsize=(14,25))

graph_titles = {'new_cases_per_100k_log': 'New cases per 100K people, log',
                'containment_health_index': 'Containment Health Index'}

for i in range(10):
    for k, var in enumerate(['new_cases_per_100k_log', 'containment_health_index']):
        month = int(i+3)
        dfnt = df[df.month == month].copy()
        sns.kdeplot(dfnt.loc[dfnt.ind_category == 'low', var], fill=True, label = 'Low', bw_adjust = .8, alpha = 0.2, ax=axs[i,k])
        sns.kdeplot(dfnt.loc[dfnt.ind_category == 'medium', var], fill=True, label = 'Medium', bw_adjust = .8, alpha = 0.2, ax=axs[i,k])
        sns.kdeplot(dfnt.loc[dfnt.ind_category == 'high', var], fill=True, label = 'High', bw_adjust = .8, alpha = 0.2, ax=axs[i,k])
        axs[i,k].set_title(f"{graph_titles[var]}, {calendar.month_name[month]}")
        axs[i,k].legend(prop={'size': 8})
  
plt.tight_layout()
fig.savefig('cases_health_dist.png')

7.6. Differences in COVID-19 rates and response

import altair as alt

df = pd.read_csv('2021-01-04 final_data.csv')
df = df[df.country != 'Tanzania'].copy()

df = df[df.country != 'Trinidad and Tobago'].copy()

df['individualism category'] = df['individualism_index'].map(lambda x: 'high' if x >= 60 else 'low' if x <= 25 else 'medium')

color_by_variable = alt.Chart(df[df.month != 2]).mark_circle(opacity=0.3).encode(
    x=alt.X('new_cases_per_100k_log:Q', axis = alt.Axis(title = 'New cases per 100 thousand people (log)')),
    y=alt.Y('containment_health_index', axis = alt.Axis(title = 'Containment health index')),
    color=alt.Color('individualism category', 
                    sort = ['low', 'medium', 'high']))

color_by_variable.properties(
) + color_by_variable.transform_regression('new_cases_per_100k_log', 'containment_health_index', 
        groupby=['individualism category']).mark_line(size=3, opacity = 0.9)